Daily Papers

Latent Diffusion Model (LDM) achieves state-of-the-art performances in image generation yet raising copyright and privacy concerns. Adversarial attacks on LDM are then born to protect unauthorized images from being used in LDM-driven few-shot generation. However, these attacks suffer from moderate performance and excessive computational cost, especially in GPU memory. In this paper, we propose an effective adversarial attack on LDM that shows superior performance against state-of-the-art few-shot generation pipeline of LDM, for example, LoRA. We implement the attack with memory efficiency by introducing several mechanisms and decrease the memory cost of the attack to less than 6GB, which allows individual users to run the attack on a majority of consumer GPUs. Our proposed attack can be a practical tool for people facing the copyright and privacy risk brought by LDM to protect themselves.

Despite the recent visually-pleasing results achieved, the massive computational cost has been a long-standing flaw for diffusion probabilistic models (DPMs), which, in turn, greatly limits their applications on resource-limited platforms. Prior methods towards efficient DPM, however, have largely focused on accelerating the testing yet overlooked their huge complexity and sizes. In this paper, we make a dedicated attempt to lighten DPM while striving to preserve its favourable performance. We start by training a small-sized latent diffusion model (LDM) from scratch, but observe a significant fidelity drop in the synthetic images. Through a thorough assessment, we find that DPM is intrinsically biased against high-frequency generation, and learns to recover different frequency components at different time-steps. These properties make compact networks unable to represent frequency dynamics with accurate high-frequency estimation. Towards this end, we introduce a customized design for slim DPM, which we term as Spectral Diffusion (SD), for light-weight image synthesis. SD incorporates wavelet gating in its architecture to enable frequency dynamic feature extraction at every reverse steps, and conducts spectrum-aware distillation to promote high-frequency recovery by inverse weighting the objective based on spectrum magni tudes. Experimental results demonstrate that, SD achieves 8-18x computational complexity reduction as compared to the latent diffusion models on a series of conditional and unconditional image generation tasks while retaining competitive image fidelity.

This paper introduces a novel framework for DNA sequence generation, comprising two key components: DiscDiff, a Latent Diffusion Model (LDM) tailored for generating discrete DNA sequences, and Absorb-Escape, a post-training algorithm designed to refine these sequences. Absorb-Escape enhances the realism of the generated sequences by correcting `round errors' inherent in the conversion process between latent and input spaces. Our approach not only sets new standards in DNA sequence generation but also demonstrates superior performance over existing diffusion models, in generating both short and long DNA sequences. Additionally, we introduce EPD-GenDNA, the first comprehensive, multi-species dataset for DNA generation, encompassing 160,000 unique sequences from 15 species. We hope this study will advance the generative modelling of DNA, with potential implications for gene therapy and protein production.

Diffusion models have recently shown the ability to generate high-quality images. However, controlling its generation process still poses challenges. The image style transfer task is one of those challenges that transfers the visual attributes of a style image to another content image. Typical obstacle of this task is the requirement of additional training of a pre-trained model. We propose a training-free style transfer algorithm, Style Tracking Reverse Diffusion Process (STRDP) for a pretrained Latent Diffusion Model (LDM). Our algorithm employs Adaptive Instance Normalization (AdaIN) function in a distinct manner during the reverse diffusion process of an LDM while tracking the encoding history of the style image. This algorithm enables style transfer in the latent space of LDM for reduced computational cost, and provides compatibility for various LDM models. Through a series of experiments and a user study, we show that our method can quickly transfer the style of an image without additional training. The speed, compatibility, and training-free aspect of our algorithm facilitates agile experiments with combinations of styles and LDMs for extensive application.

The immense scale of the recent large language models (LLM) allows many interesting properties, such as, instruction- and chain-of-thought-based fine-tuning, that has significantly improved zero- and few-shot performance in many natural language processing (NLP) tasks. Inspired by such successes, we adopt such an instruction-tuned LLM Flan-T5 as the text encoder for text-to-audio (TTA) generation -- a task where the goal is to generate an audio from its textual description. The prior works on TTA either pre-trained a joint text-audio encoder or used a non-instruction-tuned model, such as, T5. Consequently, our latent diffusion model (LDM)-based approach TANGO outperforms the state-of-the-art AudioLDM on most metrics and stays comparable on the rest on AudioCaps test set, despite training the LDM on a 63 times smaller dataset and keeping the text encoder frozen. This improvement might also be attributed to the adoption of audio pressure level-based sound mixing for training set augmentation, whereas the prior methods take a random mix.

The tremendous progress in neural image generation, coupled with the emergence of seemingly omnipotent vision-language models has finally enabled text-based interfaces for creating and editing images. Handling generic images requires a diverse underlying generative model, hence the latest works utilize diffusion models, which were shown to surpass GANs in terms of diversity. One major drawback of diffusion models, however, is their relatively slow inference time. In this paper, we present an accelerated solution to the task of local text-driven editing of generic images, where the desired edits are confined to a user-provided mask. Our solution leverages a recent text-to-image Latent Diffusion Model (LDM), which speeds up diffusion by operating in a lower-dimensional latent space. We first convert the LDM into a local image editor by incorporating Blended Diffusion into it. Next we propose an optimization-based solution for the inherent inability of this LDM to accurately reconstruct images. Finally, we address the scenario of performing local edits using thin masks. We evaluate our method against the available baselines both qualitatively and quantitatively and demonstrate that in addition to being faster, our method achieves better precision than the baselines while mitigating some of their artifacts.

Image-based head swapping task aims to stitch a source head to another source body flawlessly. This seldom-studied task faces two major challenges: 1) Preserving the head and body from various sources while generating a seamless transition region. 2) No paired head swapping dataset and benchmark so far. In this paper, we propose a semantic-mixing diffusion model for head swapping (HS-Diffusion) which consists of a latent diffusion model (LDM) and a semantic layout generator. We blend the semantic layouts of source head and source body, and then inpaint the transition region by the semantic layout generator, achieving a coarse-grained head swapping. Semantic-mixing LDM can further implement a fine-grained head swapping with the inpainted layout as condition by a progressive fusion process, while preserving head and body with high-quality reconstruction. To this end, we propose a semantic calibration strategy for natural inpainting and a neck alignment for geometric realism. Importantly, we construct a new image-based head swapping benchmark and design two tailor-designed metrics (Mask-FID and Focal-FID). Extensive experiments demonstrate the superiority of our framework. The code will be available: https://github.com/qinghew/HS-Diffusion.

Test-time adaptation (TTA) addresses the unforeseen distribution shifts occurring during test time. In TTA, performance, memory consumption, and time consumption are crucial considerations. A recent diffusion-based TTA approach for restoring corrupted images involves image-level updates. However, using pixel space diffusion significantly increases resource requirements compared to conventional model updating TTA approaches, revealing limitations as a TTA method. To address this, we propose a novel TTA method that leverages an image editing model based on a latent diffusion model (LDM) and fine-tunes it using our newly introduced corruption modeling scheme. This scheme enhances the robustness of the diffusion model against distribution shifts by creating (clean, corrupted) image pairs and fine-tuning the model to edit corrupted images into clean ones. Moreover, we introduce a distilled variant to accelerate the model for corruption editing using only 4 network function evaluations (NFEs). We extensively validated our method across various architectures and datasets including image and video domains. Our model achieves the best performance with a 100 times faster runtime than that of a diffusion-based baseline. Furthermore, it is three times faster than the previous model updating TTA method that utilizes data augmentation, making an image-level updating approach more feasible.

We introduce a novel method to automatically generate an artistic typography by stylizing one or more letter fonts to visually convey the semantics of an input word, while ensuring that the output remains readable. To address an assortment of challenges with our task at hand including conflicting goals (artistic stylization vs. legibility), lack of ground truth, and immense search space, our approach utilizes large language models to bridge texts and visual images for stylization and build an unsupervised generative model with a diffusion model backbone. Specifically, we employ the denoising generator in Latent Diffusion Model (LDM), with the key addition of a CNN-based discriminator to adapt the input style onto the input text. The discriminator uses rasterized images of a given letter/word font as real samples and output of the denoising generator as fake samples. Our model is coined DS-Fusion for discriminated and stylized diffusion. We showcase the quality and versatility of our method through numerous examples, qualitative and quantitative evaluation, as well as ablation studies. User studies comparing to strong baselines including CLIPDraw and DALL-E 2, as well as artist-crafted typographies, demonstrate strong performance of DS-Fusion.

The Video-to-Audio (V2A) model has recently gained attention for its practical application in generating audio directly from silent videos, particularly in video/film production. However, previous methods in V2A have limited generation quality in terms of temporal synchronization and audio-visual relevance. We present Diff-Foley, a synchronized Video-to-Audio synthesis method with a latent diffusion model (LDM) that generates high-quality audio with improved synchronization and audio-visual relevance. We adopt contrastive audio-visual pretraining (CAVP) to learn more temporally and semantically aligned features, then train an LDM with CAVP-aligned visual features on spectrogram latent space. The CAVP-aligned features enable LDM to capture the subtler audio-visual correlation via a cross-attention module. We further significantly improve sample quality with `double guidance'. Diff-Foley achieves state-of-the-art V2A performance on current large scale V2A dataset. Furthermore, we demonstrate Diff-Foley practical applicability and generalization capabilities via downstream finetuning. Project Page: see https://diff-foley.github.io/

Generating images from brain waves is gaining increasing attention due to its potential to advance brain-computer interface (BCI) systems by understanding how brain signals encode visual cues. Most of the literature has focused on fMRI-to-Image tasks as fMRI is characterized by high spatial resolution. However, fMRI is an expensive neuroimaging modality and does not allow for real-time BCI. On the other hand, electroencephalography (EEG) is a low-cost, non-invasive, and portable neuroimaging technique, making it an attractive option for future real-time applications. Nevertheless, EEG presents inherent challenges due to its low spatial resolution and susceptibility to noise and artifacts, which makes generating images from EEG more difficult. In this paper, we address these problems with a streamlined framework based on the ControlNet adapter for conditioning a latent diffusion model (LDM) through EEG signals. We conduct experiments and ablation studies on popular benchmarks to demonstrate that the proposed method beats other state-of-the-art models. Unlike these methods, which often require extensive preprocessing, pretraining, different losses, and captioning models, our approach is efficient and straightforward, requiring only minimal preprocessing and a few components. Code will be available after publication.

Latent Consistency Distillation (LCD) has emerged as a promising paradigm for efficient text-to-image synthesis. By distilling a latent consistency model (LCM) from a pre-trained teacher latent diffusion model (LDM), LCD facilitates the generation of high-fidelity images within merely 2 to 4 inference steps. However, the LCM's efficient inference is obtained at the cost of the sample quality. In this paper, we propose compensating the quality loss by aligning LCM's output with human preference during training. Specifically, we introduce Reward Guided LCD (RG-LCD), which integrates feedback from a reward model (RM) into the LCD process by augmenting the original LCD loss with the objective of maximizing the reward associated with LCM's single-step generation. As validated through human evaluation, when trained with the feedback of a good RM, the 2-step generations from our RG-LCM are favored by humans over the 50-step DDIM samples from the teacher LDM, representing a 25 times inference acceleration without quality loss. As directly optimizing towards differentiable RMs can suffer from over-optimization, we overcome this difficulty by proposing the use of a latent proxy RM (LRM). This novel component serves as an intermediary, connecting our LCM with the RM. Empirically, we demonstrate that incorporating the LRM into our RG-LCD successfully avoids high-frequency noise in the generated images, contributing to both improved FID on MS-COCO and a higher HPSv2.1 score on HPSv2's test set, surpassing those achieved by the baseline LCM.

We propose Magic Clothing, a latent diffusion model (LDM)-based network architecture for an unexplored garment-driven image synthesis task. Aiming at generating customized characters wearing the target garments with diverse text prompts, the image controllability is the most critical issue, i.e., to preserve the garment details and maintain faithfulness to the text prompts. To this end, we introduce a garment extractor to capture the detailed garment features, and employ self-attention fusion to incorporate them into the pretrained LDMs, ensuring that the garment details remain unchanged on the target character. Then, we leverage the joint classifier-free guidance to balance the control of garment features and text prompts over the generated results. Meanwhile, the proposed garment extractor is a plug-in module applicable to various finetuned LDMs, and it can be combined with other extensions like ControlNet and IP-Adapter to enhance the diversity and controllability of the generated characters. Furthermore, we design Matched-Points-LPIPS (MP-LPIPS), a robust metric for evaluating the consistency of the target image to the source garment. Extensive experiments demonstrate that our Magic Clothing achieves state-of-the-art results under various conditional controls for garment-driven image synthesis. Our source code is available at https://github.com/ShineChen1024/MagicClothing.

Video depth estimation lifts monocular video clips to 3D by inferring dense depth at every frame. Recent advances in single-image depth estimation, brought about by the rise of large foundation models and the use of synthetic training data, have fueled a renewed interest in video depth. However, naively applying a single-image depth estimator to every frame of a video disregards temporal continuity, which not only leads to flickering but may also break when camera motion causes sudden changes in depth range. An obvious and principled solution would be to build on top of video foundation models, but these come with their own limitations; including expensive training and inference, imperfect 3D consistency, and stitching routines for the fixed-length (short) outputs. We take a step back and demonstrate how to turn a single-image latent diffusion model (LDM) into a state-of-the-art video depth estimator. Our model, which we call RollingDepth, has two main ingredients: (i) a multi-frame depth estimator that is derived from a single-image LDM and maps very short video snippets (typically frame triplets) to depth snippets. (ii) a robust, optimization-based registration algorithm that optimally assembles depth snippets sampled at various different frame rates back into a consistent video. RollingDepth is able to efficiently handle long videos with hundreds of frames and delivers more accurate depth videos than both dedicated video depth estimators and high-performing single-frame models. Project page: rollingdepth.github.io.

This paper introduces ViscoNet, a novel method that enhances text-to-image human generation models with visual prompting. Unlike existing methods that rely on lengthy text descriptions to control the image structure, ViscoNet allows users to specify the visual appearance of the target object with a reference image. ViscoNet disentangles the object's appearance from the image background and injects it into a pre-trained latent diffusion model (LDM) model via a ControlNet branch. This way, ViscoNet mitigates the style mode collapse problem and enables precise and flexible visual control. We demonstrate the effectiveness of ViscoNet on human image generation, where it can manipulate visual attributes and artistic styles with text and image prompts. We also show that ViscoNet can learn visual conditioning from small and specific object domains while preserving the generative power of the LDM backbone.

Recently, with the tremendous success of diffusion models in the field of text-to-image (T2I) generation, increasing attention has been directed toward their potential in text-to-video (T2V) applications. However, the computational demands of diffusion models pose significant challenges, particularly in generating high-resolution videos with high frame rates. In this paper, we propose CascadeV, a cascaded latent diffusion model (LDM), that is capable of producing state-of-the-art 2K resolution videos. Experiments demonstrate that our cascaded model achieves a higher compression ratio, substantially reducing the computational challenges associated with high-quality video generation. We also implement a spatiotemporal alternating grid 3D attention mechanism, which effectively integrates spatial and temporal information, ensuring superior consistency across the generated video frames. Furthermore, our model can be cascaded with existing T2V models, theoretically enabling a 4times increase in resolution or frames per second without any fine-tuning. Our code is available at https://github.com/bytedance/CascadeV.

We present xGen-VideoSyn-1, a text-to-video (T2V) generation model capable of producing realistic scenes from textual descriptions. Building on recent advancements, such as OpenAI's Sora, we explore the latent diffusion model (LDM) architecture and introduce a video variational autoencoder (VidVAE). VidVAE compresses video data both spatially and temporally, significantly reducing the length of visual tokens and the computational demands associated with generating long-sequence videos. To further address the computational costs, we propose a divide-and-merge strategy that maintains temporal consistency across video segments. Our Diffusion Transformer (DiT) model incorporates spatial and temporal self-attention layers, enabling robust generalization across different timeframes and aspect ratios. We have devised a data processing pipeline from the very beginning and collected over 13M high-quality video-text pairs. The pipeline includes multiple steps such as clipping, text detection, motion estimation, aesthetics scoring, and dense captioning based on our in-house video-LLM model. Training the VidVAE and DiT models required approximately 40 and 642 H100 days, respectively. Our model supports over 14-second 720p video generation in an end-to-end way and demonstrates competitive performance against state-of-the-art T2V models.

High-resolution 3D object generation remains a challenging task primarily due to the limited availability of comprehensive annotated training data. Recent advancements have aimed to overcome this constraint by harnessing image generative models, pretrained on extensive curated web datasets, using knowledge transfer techniques like Score Distillation Sampling (SDS). Efficiently addressing the requirements of high-resolution rendering often necessitates the adoption of latent representation-based models, such as the Latent Diffusion Model (LDM). In this framework, a significant challenge arises: To compute gradients for individual image pixels, it is necessary to backpropagate gradients from the designated latent space through the frozen components of the image model, such as the VAE encoder used within LDM. However, this gradient propagation pathway has never been optimized, remaining uncontrolled during training. We find that the unregulated gradients adversely affect the 3D model's capacity in acquiring texture-related information from the image generative model, leading to poor quality appearance synthesis. To address this overarching challenge, we propose an innovative operation termed Pixel-wise Gradient Clipping (PGC) designed for seamless integration into existing 3D generative models, thereby enhancing their synthesis quality. Specifically, we control the magnitude of stochastic gradients by clipping the pixel-wise gradients efficiently, while preserving crucial texture-related gradient directions. Despite this simplicity and minimal extra cost, extensive experiments demonstrate the efficacy of our PGC in enhancing the performance of existing 3D generative models for high-resolution object rendering.

Recently, there has been a significant advancement in text-to-image diffusion models, leading to groundbreaking performance in 2D image generation. These advancements have been extended to 3D models, enabling the generation of novel 3D objects from textual descriptions. This has evolved into NeRF editing methods, which allow the manipulation of existing 3D objects through textual conditioning. However, existing NeRF editing techniques have faced limitations in their performance due to slow training speeds and the use of loss functions that do not adequately consider editing. To address this, here we present a novel 3D NeRF editing approach dubbed ED-NeRF by successfully embedding real-world scenes into the latent space of the latent diffusion model (LDM) through a unique refinement layer. This approach enables us to obtain a NeRF backbone that is not only faster but also more amenable to editing compared to traditional image space NeRF editing. Furthermore, we propose an improved loss function tailored for editing by migrating the delta denoising score (DDS) distillation loss, originally used in 2D image editing to the three-dimensional domain. This novel loss function surpasses the well-known score distillation sampling (SDS) loss in terms of suitability for editing purposes. Our experimental results demonstrate that ED-NeRF achieves faster editing speed while producing improved output quality compared to state-of-the-art 3D editing models.

Multistep instructions, such as recipes and how-to guides, greatly benefit from visual aids, such as a series of images that accompany the instruction steps. While Large Language Models (LLMs) have become adept at generating coherent textual steps, Large Vision/Language Models (LVLMs) are less capable of generating accompanying image sequences. The most challenging aspect is that each generated image needs to adhere to the relevant textual step instruction, as well as be visually consistent with earlier images in the sequence. To address this problem, we propose an approach for generating consistent image sequences, which integrates a Latent Diffusion Model (LDM) with an LLM to transform the sequence into a caption to maintain the semantic coherence of the sequence. In addition, to maintain the visual coherence of the image sequence, we introduce a copy mechanism to initialise reverse diffusion processes with a latent vector iteration from a previously generated image from a relevant step. Both strategies will condition the reverse diffusion process on the sequence of instruction steps and tie the contents of the current image to previous instruction steps and corresponding images. Experiments show that the proposed approach is preferred by humans in 46.6% of the cases against 26.6% for the second best method. In addition, automatic metrics showed that the proposed method maintains semantic coherence and visual consistency across steps in both domains.

Text-to-image generative models have made remarkable advancements in generating high-quality images. However, generated images often contain undesirable artifacts or other errors due to model limitations. Existing techniques to fine-tune generated images are time-consuming (manual editing), produce poorly-integrated results (inpainting), or result in unexpected changes across the entire image (variation selection and prompt fine-tuning). In this work, we present Diffusion Brush, a Latent Diffusion Model-based (LDM) tool to efficiently fine-tune desired regions within an AI-synthesized image. Our method introduces new random noise patterns at targeted regions during the reverse diffusion process, enabling the model to efficiently make changes to the specified regions while preserving the original context for the rest of the image. We evaluate our method's usability and effectiveness through a user study with artists, comparing our technique against other state-of-the-art image inpainting techniques and editing software for fine-tuning AI-generated imagery.

Previous efforts have managed to generate production-ready 3D assets from text or images. However, these methods primarily employ NeRF or 3D Gaussian representations, which are not adept at producing smooth, high-quality geometries required by modern rendering pipelines. In this paper, we propose LDM, a novel feed-forward framework capable of generating high-fidelity, illumination-decoupled textured mesh from a single image or text prompts. We firstly utilize a multi-view diffusion model to generate sparse multi-view inputs from single images or text prompts, and then a transformer-based model is trained to predict a tensorial SDF field from these sparse multi-view image inputs. Finally, we employ a gradient-based mesh optimization layer to refine this model, enabling it to produce an SDF field from which high-quality textured meshes can be extracted. Extensive experiments demonstrate that our method can generate diverse, high-quality 3D mesh assets with corresponding decomposed RGB textures within seconds.

Latent diffusion models (LDMs) exhibit an impressive ability to produce realistic images, yet the inner workings of these models remain mysterious. Even when trained purely on images without explicit depth information, they typically output coherent pictures of 3D scenes. In this work, we investigate a basic interpretability question: does an LDM create and use an internal representation of simple scene geometry? Using linear probes, we find evidence that the internal activations of the LDM encode linear representations of both 3D depth data and a salient-object / background distinction. These representations appear surprisingly early in the denoising process-well before a human can easily make sense of the noisy images. Intervention experiments further indicate these representations play a causal role in image synthesis, and may be used for simple high-level editing of an LDM's output. Project page: https://yc015.github.io/scene-representation-diffusion-model/

Latent Diffusion Models (LDMs) enable high-quality image synthesis while avoiding excessive compute demands by training a diffusion model in a compressed lower-dimensional latent space. Here, we apply the LDM paradigm to high-resolution video generation, a particularly resource-intensive task. We first pre-train an LDM on images only; then, we turn the image generator into a video generator by introducing a temporal dimension to the latent space diffusion model and fine-tuning on encoded image sequences, i.e., videos. Similarly, we temporally align diffusion model upsamplers, turning them into temporally consistent video super resolution models. We focus on two relevant real-world applications: Simulation of in-the-wild driving data and creative content creation with text-to-video modeling. In particular, we validate our Video LDM on real driving videos of resolution 512 x 1024, achieving state-of-the-art performance. Furthermore, our approach can easily leverage off-the-shelf pre-trained image LDMs, as we only need to train a temporal alignment model in that case. Doing so, we turn the publicly available, state-of-the-art text-to-image LDM Stable Diffusion into an efficient and expressive text-to-video model with resolution up to 1280 x 2048. We show that the temporal layers trained in this way generalize to different fine-tuned text-to-image LDMs. Utilizing this property, we show the first results for personalized text-to-video generation, opening exciting directions for future content creation. Project page: https://research.nvidia.com/labs/toronto-ai/VideoLDM/

Novel diffusion models can synthesize photo-realistic images with integrated high-quality text. Surprisingly, we demonstrate through attention activation patching that only less than 1% of diffusion models' parameters, all contained in attention layers, influence the generation of textual content within the images. Building on this observation, we improve textual generation efficiency and performance by targeting cross and joint attention layers of diffusion models. We introduce several applications that benefit from localizing the layers responsible for textual content generation. We first show that a LoRA-based fine-tuning solely of the localized layers enhances, even more, the general text-generation capabilities of large diffusion models while preserving the quality and diversity of the diffusion models' generations. Then, we demonstrate how we can use the localized layers to edit textual content in generated images. Finally, we extend this idea to the practical use case of preventing the generation of toxic text in a cost-free manner. In contrast to prior work, our localization approach is broadly applicable across various diffusion model architectures, including U-Net (e.g., LDM and SDXL) and transformer-based (e.g., DeepFloyd IF and Stable Diffusion 3), utilizing diverse text encoders (e.g., from CLIP to the large language models like T5). Project page available at https://t2i-text-loc.github.io/.

Conditioned diffusion models have demonstrated state-of-the-art text-to-image synthesis capacity. Recently, most works focus on synthesizing independent images; While for real-world applications, it is common and necessary to generate a series of coherent images for story-stelling. In this work, we mainly focus on story visualization and continuation tasks and propose AR-LDM, a latent diffusion model auto-regressively conditioned on history captions and generated images. Moreover, AR-LDM can generalize to new characters through adaptation. To our best knowledge, this is the first work successfully leveraging diffusion models for coherent visual story synthesizing. Quantitative results show that AR-LDM achieves SoTA FID scores on PororoSV, FlintstonesSV, and the newly introduced challenging dataset VIST containing natural images. Large-scale human evaluations show that AR-LDM has superior performance in terms of quality, relevance, and consistency.

We introduce LlamaGen, a new family of image generation models that apply original ``next-token prediction'' paradigm of large language models to visual generation domain. It is an affirmative answer to whether vanilla autoregressive models, e.g., Llama, without inductive biases on visual signals can achieve state-of-the-art image generation performance if scaling properly. We reexamine design spaces of image tokenizers, scalability properties of image generation models, and their training data quality. The outcome of this exploration consists of: (1) An image tokenizer with downsample ratio of 16, reconstruction quality of 0.94 rFID and codebook usage of 97% on ImageNet benchmark. (2) A series of class-conditional image generation models ranging from 111M to 3.1B parameters, achieving 2.18 FID on ImageNet 256x256 benchmarks, outperforming the popular diffusion models such as LDM, DiT. (3) A text-conditional image generation model with 775M parameters, from two-stage training on LAION-COCO and high aesthetics quality images, demonstrating competitive performance of visual quality and text alignment. (4) We verify the effectiveness of LLM serving frameworks in optimizing the inference speed of image generation models and achieve 326% - 414% speedup. We release all models and codes to facilitate open-source community of visual generation and multimodal foundation models.

Reverse sampling and score-distillation have emerged as main workhorses in recent years for image manipulation using latent diffusion models (LDMs). While reverse diffusion sampling often requires adjustments of LDM architecture or feature engineering, score distillation offers a simple yet powerful model-agnostic approach, but it is often prone to mode-collapsing. To address these limitations and leverage the strengths of both approaches, here we introduce a novel framework called {\em DreamSampler}, which seamlessly integrates these two distinct approaches through the lens of regularized latent optimization. Similar to score-distillation, DreamSampler is a model-agnostic approach applicable to any LDM architecture, but it allows both distillation and reverse sampling with additional guidance for image editing and reconstruction. Through experiments involving image editing, SVG reconstruction and etc, we demonstrate the competitive performance of DreamSampler compared to existing approaches, while providing new applications.

Generating complete 360-degree panoramas from narrow field of view images is ongoing research as omnidirectional RGB data is not readily available. Existing GAN-based approaches face some barriers to achieving higher quality output, and have poor generalization performance over different mask types. In this paper, we present our 360-degree indoor RGB-D panorama outpainting model using latent diffusion models (LDM), called PanoDiffusion. We introduce a new bi-modal latent diffusion structure that utilizes both RGB and depth panoramic data during training, which works surprisingly well to outpaint depth-free RGB images during inference. We further propose a novel technique of introducing progressive camera rotations during each diffusion denoising step, which leads to substantial improvement in achieving panorama wraparound consistency. Results show that our PanoDiffusion not only significantly outperforms state-of-the-art methods on RGB-D panorama outpainting by producing diverse well-structured results for different types of masks, but can also synthesize high-quality depth panoramas to provide realistic 3D indoor models.

Inspired by the remarkable success of Latent Diffusion Models (LDMs) for image synthesis, we study LDM for text-to-video generation, which is a formidable challenge due to the computational and memory constraints during both model training and inference. A single LDM is usually only capable of generating a very limited number of video frames. Some existing works focus on separate prediction models for generating more video frames, which suffer from additional training cost and frame-level jittering, however. In this paper, we propose a framework called "Reuse and Diffuse" dubbed VidRD to produce more frames following the frames already generated by an LDM. Conditioned on an initial video clip with a small number of frames, additional frames are iteratively generated by reusing the original latent features and following the previous diffusion process. Besides, for the autoencoder used for translation between pixel space and latent space, we inject temporal layers into its decoder and fine-tune these layers for higher temporal consistency. We also propose a set of strategies for composing video-text data that involve diverse content from multiple existing datasets including video datasets for action recognition and image-text datasets. Extensive experiments show that our method achieves good results in both quantitative and qualitative evaluations. Our project page is available https://anonymous0x233.github.io/ReuseAndDiffuse/{here}.

There exists recent work in computer vision, named VAR, that proposes a new autoregressive paradigm for image generation. Diverging from the vanilla next-token prediction, VAR structurally reformulates the image generation into a coarse to fine next-scale prediction. In this paper, we show that this scale-wise autoregressive framework can be effectively decoupled into intra-scale modeling, which captures local spatial dependencies within each scale, and inter-scale modeling, which models cross-scale relationships progressively from coarse-to-fine scales. This decoupling structure allows to rebuild VAR in a more computationally efficient manner. Specifically, for intra-scale modeling -- crucial for generating high-fidelity images -- we retain the original bidirectional self-attention design to ensure comprehensive modeling; for inter-scale modeling, which semantically connects different scales but is computationally intensive, we apply linear-complexity mechanisms like Mamba to substantially reduce computational overhead. We term this new framework M-VAR. Extensive experiments demonstrate that our method outperforms existing models in both image quality and generation speed. For example, our 1.5B model, with fewer parameters and faster inference speed, outperforms the largest VAR-d30-2B. Moreover, our largest model M-VAR-d32 impressively registers 1.78 FID on ImageNet 256times256 and outperforms the prior-art autoregressive models LlamaGen/VAR by 0.4/0.19 and popular diffusion models LDM/DiT by 1.82/0.49, respectively. Code is avaiable at https://github.com/OliverRensu/MVAR.

Diffusion models have recently revolutionized the field of image synthesis due to their ability to generate photorealistic images. However, one of the major drawbacks of diffusion models is that the image generation process is costly. A large image-to-image network has to be applied many times to iteratively refine an image from random noise. While many recent works propose techniques to reduce the number of required steps, they generally treat the underlying denoising network as a black box. In this work, we investigate the behavior of the layers within the network and find that 1) the layers' output changes smoothly over time, 2) the layers show distinct patterns of change, and 3) the change from step to step is often very small. We hypothesize that many layer computations in the denoising network are redundant. Leveraging this, we introduce block caching, in which we reuse outputs from layer blocks of previous steps to speed up inference. Furthermore, we propose a technique to automatically determine caching schedules based on each block's changes over timesteps. In our experiments, we show through FID, human evaluation and qualitative analysis that Block Caching allows to generate images with higher visual quality at the same computational cost. We demonstrate this for different state-of-the-art models (LDM and EMU) and solvers (DDIM and DPM).

In recent years, diffusion models have become one of the main methods for generating images. However, detecting images generated by these models remains a challenging task. This paper proposes a novel method for detecting images generated by Latent Diffusion Models (LDM) by identifying artifacts introduced by their autoencoders. By training a detector to distinguish between real images and those reconstructed by the LDM autoencoder, the method enables detection of generated images without directly training on them. The novelty of this research lies in the fact that, unlike similar approaches, this method does not require training on synthesized data, significantly reducing computational costs and enhancing generalization ability. Experimental results show high detection accuracy with minimal false positives, making this approach a promising tool for combating fake images.

While generative diffusion models excel in producing high-quality images, they can also be misused to mimic authorized images, posing a significant threat to AI systems. Efforts have been made to add calibrated perturbations to protect images from diffusion-based mimicry pipelines. However, most of the existing methods are too ineffective and even impractical to be used by individual users due to their high computation and memory requirements. In this work, we present novel findings on attacking latent diffusion models (LDM) and propose new plug-and-play strategies for more effective protection. In particular, we explore the bottleneck in attacking an LDM, discovering that the encoder module rather than the denoiser module is the vulnerable point. Based on this insight, we present our strategy using Score Distillation Sampling (SDS) to double the speed of protection and reduce memory occupation by half without compromising its strength. Additionally, we provide a robust protection strategy by counterintuitively minimizing the semantic loss, which can assist in generating more natural perturbations. Finally, we conduct extensive experiments to substantiate our findings and comprehensively evaluate our newly proposed strategies. We hope our insights and protective measures can contribute to better defense against malicious diffusion-based mimicry, advancing the development of secure AI systems. The code is available in https://github.com/xavihart/Diff-Protect

With generative models producing high quality images that are indistinguishable from real ones, there is growing concern regarding the malicious usage of AI-generated images. Imperceptible image watermarking is one viable solution towards such concerns. Prior watermarking methods map the image to a latent space for adding the watermark. Moreover, Latent Diffusion Models (LDM) generate the image in the latent space of a pre-trained autoencoder. We argue that this latent space can be used to integrate watermarking into the generation process. To this end, we present LaWa, an in-generation image watermarking method designed for LDMs. By using coarse-to-fine watermark embedding modules, LaWa modifies the latent space of pre-trained autoencoders and achieves high robustness against a wide range of image transformations while preserving perceptual quality of the image. We show that LaWa can also be used as a general image watermarking method. Through extensive experiments, we demonstrate that LaWa outperforms previous works in perceptual quality, robustness against attacks, and computational complexity, while having very low false positive rate. Code is available here.

This work challenges the residual prediction paradigm in visual autoregressive modeling and presents FlexVAR, a new Flexible Visual AutoRegressive image generation paradigm. FlexVAR facilitates autoregressive learning with ground-truth prediction, enabling each step to independently produce plausible images. This simple, intuitive approach swiftly learns visual distributions and makes the generation process more flexible and adaptable. Trained solely on low-resolution images (leq 256px), FlexVAR can: (1) Generate images of various resolutions and aspect ratios, even exceeding the resolution of the training images. (2) Support various image-to-image tasks, including image refinement, in/out-painting, and image expansion. (3) Adapt to various autoregressive steps, allowing for faster inference with fewer steps or enhancing image quality with more steps. Our 1.0B model outperforms its VAR counterpart on the ImageNet 256times256 benchmark. Moreover, when zero-shot transfer the image generation process with 13 steps, the performance further improves to 2.08 FID, outperforming state-of-the-art autoregressive models AiM/VAR by 0.25/0.28 FID and popular diffusion models LDM/DiT by 1.52/0.19 FID, respectively. When transferring our 1.0B model to the ImageNet 512times512 benchmark in a zero-shot manner, FlexVAR achieves competitive results compared to the VAR 2.3B model, which is a fully supervised model trained at 512times512 resolution.

Latent Diffusion Models (LDMs) are known to have an unstable generation process, where even small perturbations or shifts in the input noise can lead to significantly different outputs. This hinders their applicability in applications requiring consistent results. In this work, we redesign LDMs to enhance consistency by making them shift-equivariant. While introducing anti-aliasing operations can partially improve shift-equivariance, significant aliasing and inconsistency persist due to the unique challenges in LDMs, including 1) aliasing amplification during VAE training and multiple U-Net inferences, and 2) self-attention modules that inherently lack shift-equivariance. To address these issues, we redesign the attention modules to be shift-equivariant and propose an equivariance loss that effectively suppresses the frequency bandwidth of the features in the continuous domain. The resulting alias-free LDM (AF-LDM) achieves strong shift-equivariance and is also robust to irregular warping. Extensive experiments demonstrate that AF-LDM produces significantly more consistent results than vanilla LDM across various applications, including video editing and image-to-image translation. Code is available at: https://github.com/SingleZombie/AFLDM

Latent Diffusion Models (LDMs) capture the dynamic evolution of latent variables over time, blending patterns and multimodality in a generative system. Despite the proficiency of LDM in various applications, such as text-to-image generation, facilitated by robust text encoders and a variational autoencoder, the critical need to deploy large generative models on edge devices compels a search for more compact yet effective alternatives. Post Training Quantization (PTQ), a method to compress the operational size of deep learning models, encounters challenges when applied to LDM due to temporal and structural complexities. This study proposes a quantization strategy that efficiently quantize LDMs, leveraging Signal-to-Quantization-Noise Ratio (SQNR) as a pivotal metric for evaluation. By treating the quantization discrepancy as relative noise and identifying sensitive part(s) of a model, we propose an efficient quantization approach encompassing both global and local strategies. The global quantization process mitigates relative quantization noise by initiating higher-precision quantization on sensitive blocks, while local treatments address specific challenges in quantization-sensitive and time-sensitive modules. The outcomes of our experiments reveal that the implementation of both global and local treatments yields a highly efficient and effective Post Training Quantization (PTQ) of LDMs.

Modern learning-based approaches to 3D-aware image synthesis achieve high photorealism and 3D-consistent viewpoint changes for the generated images. Existing approaches represent instances in a shared canonical space. However, for in-the-wild datasets a shared canonical system can be difficult to define or might not even exist. In this work, we instead model instances in view space, alleviating the need for posed images and learned camera distributions. We find that in this setting, existing GAN-based methods are prone to generating flat geometry and struggle with distribution coverage. We hence propose WildFusion, a new approach to 3D-aware image synthesis based on latent diffusion models (LDMs). We first train an autoencoder that infers a compressed latent representation, which additionally captures the images' underlying 3D structure and enables not only reconstruction but also novel view synthesis. To learn a faithful 3D representation, we leverage cues from monocular depth prediction. Then, we train a diffusion model in the 3D-aware latent space, thereby enabling synthesis of high-quality 3D-consistent image samples, outperforming recent state-of-the-art GAN-based methods. Importantly, our 3D-aware LDM is trained without any direct supervision from multiview images or 3D geometry and does not require posed images or learned pose or camera distributions. It directly learns a 3D representation without relying on canonical camera coordinates. This opens up promising research avenues for scalable 3D-aware image synthesis and 3D content creation from in-the-wild image data. See https://katjaschwarz.github.io/wildfusion for videos of our 3D results.

Diffusion models have recently gained unprecedented attention in the field of image synthesis due to their remarkable generative capabilities. Notwithstanding their prowess, these models often incur substantial computational costs, primarily attributed to the sequential denoising process and cumbersome model size. Traditional methods for compressing diffusion models typically involve extensive retraining, presenting cost and feasibility challenges. In this paper, we introduce DeepCache, a novel training-free paradigm that accelerates diffusion models from the perspective of model architecture. DeepCache capitalizes on the inherent temporal redundancy observed in the sequential denoising steps of diffusion models, which caches and retrieves features across adjacent denoising stages, thereby curtailing redundant computations. Utilizing the property of the U-Net, we reuse the high-level features while updating the low-level features in a very cheap way. This innovative strategy, in turn, enables a speedup factor of 2.3times for Stable Diffusion v1.5 with only a 0.05 decline in CLIP Score, and 4.1times for LDM-4-G with a slight decrease of 0.22 in FID on ImageNet. Our experiments also demonstrate DeepCache's superiority over existing pruning and distillation methods that necessitate retraining and its compatibility with current sampling techniques. Furthermore, we find that under the same throughput, DeepCache effectively achieves comparable or even marginally improved results with DDIM or PLMS. The code is available at https://github.com/horseee/DeepCache

We study the scaling properties of latent diffusion models (LDMs) with an emphasis on their sampling efficiency. While improved network architecture and inference algorithms have shown to effectively boost sampling efficiency of diffusion models, the role of model size -- a critical determinant of sampling efficiency -- has not been thoroughly examined. Through empirical analysis of established text-to-image diffusion models, we conduct an in-depth investigation into how model size influences sampling efficiency across varying sampling steps. Our findings unveil a surprising trend: when operating under a given inference budget, smaller models frequently outperform their larger equivalents in generating high-quality results. Moreover, we extend our study to demonstrate the generalizability of the these findings by applying various diffusion samplers, exploring diverse downstream tasks, evaluating post-distilled models, as well as comparing performance relative to training compute. These findings open up new pathways for the development of LDM scaling strategies which can be employed to enhance generative capabilities within limited inference budgets.

Large, pretrained latent diffusion models (LDMs) have demonstrated an extraordinary ability to generate creative content, specialize to user data through few-shot fine-tuning, and condition their output on other modalities, such as semantic maps. However, are they usable as large-scale data generators, e.g., to improve tasks in the perception stack, like semantic segmentation? We investigate this question in the context of autonomous driving, and answer it with a resounding "yes". We propose an efficient data generation pipeline termed DGInStyle. First, we examine the problem of specializing a pretrained LDM to semantically-controlled generation within a narrow domain. Second, we design a Multi-resolution Latent Fusion technique to overcome the bias of LDMs towards dominant objects. Third, we propose a Style Swap technique to endow the rich generative prior with the learned semantic control. Using DGInStyle, we generate a diverse dataset of street scenes, train a domain-agnostic semantic segmentation model on it, and evaluate the model on multiple popular autonomous driving datasets. Our approach consistently increases the performance of several domain generalization methods, in some cases by +2.5 mIoU compared to the previous state-of-the-art method without our generative augmentation scheme. Source code and dataset are available at https://dginstyle.github.io .

Diffusion models have demonstrated impressive generative capabilities, but their exposure bias problem, described as the input mismatch between training and sampling, lacks in-depth exploration. In this paper, we systematically investigate the exposure bias problem in diffusion models by first analytically modelling the sampling distribution, based on which we then attribute the prediction error at each sampling step as the root cause of the exposure bias issue. Furthermore, we discuss potential solutions to this issue and propose an intuitive metric for it. Along with the elucidation of exposure bias, we propose a simple, yet effective, training-free method called Epsilon Scaling to alleviate the exposure bias. We show that Epsilon Scaling explicitly moves the sampling trajectory closer to the vector field learned in the training phase by scaling down the network output (Epsilon), mitigating the input mismatch between training and sampling. Experiments on various diffusion frameworks (ADM, DDPM/DDIM, EDM, LDM), unconditional and conditional settings, and deterministic vs. stochastic sampling verify the effectiveness of our method. Remarkably, our ADM-ES, as a SOTA stochastic sampler, obtains 2.17 FID on CIFAR-10 under 100-step unconditional generation. The code is available at https://github.com/forever208/ADM-ES and https://github.com/forever208/EDM-ES.

Latent Diffusion Models (LDMs) are renowned for their powerful capabilities in image and video synthesis. Yet, video editing methods suffer from insufficient pre-training data or video-by-video re-training cost. In addressing this gap, we propose FLDM (Fused Latent Diffusion Model), a training-free framework to achieve text-guided video editing by applying off-the-shelf image editing methods in video LDMs. Specifically, FLDM fuses latents from an image LDM and an video LDM during the denoising process. In this way, temporal consistency can be kept with video LDM while high-fidelity from the image LDM can also be exploited. Meanwhile, FLDM possesses high flexibility since both image LDM and video LDM can be replaced so advanced image editing methods such as InstructPix2Pix and ControlNet can be exploited. To the best of our knowledge, FLDM is the first method to adapt off-the-shelf image editing methods into video LDMs for video editing. Extensive quantitative and qualitative experiments demonstrate that FLDM can improve the textual alignment and temporal consistency of edited videos.

Diffusion models have demonstrated remarkable capabilities in image synthesis and related generative tasks. Nevertheless, their practicality for low-latency real-world applications is constrained by substantial computational costs and latency issues. Quantization is a dominant way to compress and accelerate diffusion models, where post-training quantization (PTQ) and quantization-aware training (QAT) are two main approaches, each bearing its own properties. While PTQ exhibits efficiency in terms of both time and data usage, it may lead to diminished performance in low bit-width. On the other hand, QAT can alleviate performance degradation but comes with substantial demands on computational and data resources. To capitalize on the advantages while avoiding their respective drawbacks, we introduce a data-free and parameter-efficient fine-tuning framework for low-bit diffusion models, dubbed EfficientDM, to achieve QAT-level performance with PTQ-like efficiency. Specifically, we propose a quantization-aware variant of the low-rank adapter (QALoRA) that can be merged with model weights and jointly quantized to low bit-width. The fine-tuning process distills the denoising capabilities of the full-precision model into its quantized counterpart, eliminating the requirement for training data. We also introduce scale-aware optimization and employ temporal learned step-size quantization to further enhance performance. Extensive experimental results demonstrate that our method significantly outperforms previous PTQ-based diffusion models while maintaining similar time and data efficiency. Specifically, there is only a marginal 0.05 sFID increase when quantizing both weights and activations of LDM-4 to 4-bit on ImageNet 256x256. Compared to QAT-based methods, our EfficientDM also boasts a 16.2x faster quantization speed with comparable generation quality.

Text-to-video is a rapidly growing research area that aims to generate a semantic, identical, and temporal coherence sequence of frames that accurately align with the input text prompt. This study focuses on zero-shot text-to-video generation considering the data- and cost-efficient. To generate a semantic-coherent video, exhibiting a rich portrayal of temporal semantics such as the whole process of flower blooming rather than a set of "moving images", we propose a novel Free-Bloom pipeline that harnesses large language models (LLMs) as the director to generate a semantic-coherence prompt sequence, while pre-trained latent diffusion models (LDMs) as the animator to generate the high fidelity frames. Furthermore, to ensure temporal and identical coherence while maintaining semantic coherence, we propose a series of annotative modifications to adapting LDMs in the reverse process, including joint noise sampling, step-aware attention shift, and dual-path interpolation. Without any video data and training requirements, Free-Bloom generates vivid and high-quality videos, awe-inspiring in generating complex scenes with semantic meaningful frame sequences. In addition, Free-Bloom is naturally compatible with LDMs-based extensions.

Latent diffusion models (LDMs) power state-of-the-art high-resolution generative image models. LDMs learn the data distribution in the latent space of an autoencoder (AE) and produce images by mapping the generated latents into RGB image space using the AE decoder. While this approach allows for efficient model training and sampling, it induces a disconnect between the training of the diffusion model and the decoder, resulting in a loss of detail in the generated images. To remediate this disconnect, we propose to leverage the internal features of the decoder to define a latent perceptual loss (LPL). This loss encourages the models to create sharper and more realistic images. Our loss can be seamlessly integrated with common autoencoders used in latent diffusion models, and can be applied to different generative modeling paradigms such as DDPM with epsilon and velocity prediction, as well as flow matching. Extensive experiments with models trained on three datasets at 256 and 512 resolution show improved quantitative -- with boosts between 6% and 20% in FID -- and qualitative results when using our perceptual loss.

Latent Diffusion models (LDMs) have achieved remarkable results in synthesizing high-resolution images. However, the iterative sampling process is computationally intensive and leads to slow generation. Inspired by Consistency Models (song et al.), we propose Latent Consistency Models (LCMs), enabling swift inference with minimal steps on any pre-trained LDMs, including Stable Diffusion (rombach et al). Viewing the guided reverse diffusion process as solving an augmented probability flow ODE (PF-ODE), LCMs are designed to directly predict the solution of such ODE in latent space, mitigating the need for numerous iterations and allowing rapid, high-fidelity sampling. Efficiently distilled from pre-trained classifier-free guided diffusion models, a high-quality 768 x 768 2~4-step LCM takes only 32 A100 GPU hours for training. Furthermore, we introduce Latent Consistency Fine-tuning (LCF), a novel method that is tailored for fine-tuning LCMs on customized image datasets. Evaluation on the LAION-5B-Aesthetics dataset demonstrates that LCMs achieve state-of-the-art text-to-image generation performance with few-step inference. Project Page: https://latent-consistency-models.github.io/

Latent Diffusion Models (LDMs) have emerged as powerful generative models, known for delivering remarkable results under constrained computational resources. However, deploying LDMs on resource-limited devices remains a complex issue, presenting challenges such as memory consumption and inference speed. To address this issue, we introduce LD-Pruner, a novel performance-preserving structured pruning method for compressing LDMs. Traditional pruning methods for deep neural networks are not tailored to the unique characteristics of LDMs, such as the high computational cost of training and the absence of a fast, straightforward and task-agnostic method for evaluating model performance. Our method tackles these challenges by leveraging the latent space during the pruning process, enabling us to effectively quantify the impact of pruning on model performance, independently of the task at hand. This targeted pruning of components with minimal impact on the output allows for faster convergence during training, as the model has less information to re-learn, thereby addressing the high computational cost of training. Consequently, our approach achieves a compressed model that offers improved inference speed and reduced parameter count, while maintaining minimal performance degradation. We demonstrate the effectiveness of our approach on three different tasks: text-to-image (T2I) generation, Unconditional Image Generation (UIG) and Unconditional Audio Generation (UAG). Notably, we reduce the inference time of Stable Diffusion (SD) by 34.9% while simultaneously improving its FID by 5.2% on MS-COCO T2I benchmark. This work paves the way for more efficient pruning methods for LDMs, enhancing their applicability.

Recent generative models have demonstrated impressive capabilities in generating realistic and visually pleasing images grounded on textual prompts. Nevertheless, a significant challenge remains in applying these models for the more intricate task of story visualization. Since it requires resolving pronouns (he, she, they) in the frame descriptions, i.e., anaphora resolution, and ensuring consistent characters and background synthesis across frames. Yet, the emerging Large Language Model (LLM) showcases robust reasoning abilities to navigate through ambiguous references and process extensive sequences. Therefore, we introduce StoryGPT-V, which leverages the merits of the latent diffusion (LDM) and LLM to produce images with consistent and high-quality characters grounded on given story descriptions. First, we train a character-aware LDM, which takes character-augmented semantic embedding as input and includes the supervision of the cross-attention map using character segmentation masks, aiming to enhance character generation accuracy and faithfulness. In the second stage, we enable an alignment between the output of LLM and the character-augmented embedding residing in the input space of the first-stage model. This harnesses the reasoning ability of LLM to address ambiguous references and the comprehension capability to memorize the context. We conduct comprehensive experiments on two visual story visualization benchmarks. Our model reports superior quantitative results and consistently generates accurate characters of remarkable quality with low memory consumption. Our code will be made publicly available.

We introduce the Joint Video-Image Diffusion model (JVID), a novel approach to generating high-quality and temporally coherent videos. We achieve this by integrating two diffusion models: a Latent Image Diffusion Model (LIDM) trained on images and a Latent Video Diffusion Model (LVDM) trained on video data. Our method combines these models in the reverse diffusion process, where the LIDM enhances image quality and the LVDM ensures temporal consistency. This unique combination allows us to effectively handle the complex spatio-temporal dynamics in video generation. Our results demonstrate quantitative and qualitative improvements in producing realistic and coherent videos.

Score-based diffusion models are a class of generative models whose dynamics is described by stochastic differential equations that map noise into data. While recent works have started to lay down a theoretical foundation for these models, an analytical understanding of the role of the diffusion time T is still lacking. Current best practice advocates for a large T to ensure that the forward dynamics brings the diffusion sufficiently close to a known and simple noise distribution; however, a smaller value of T should be preferred for a better approximation of the score-matching objective and higher computational efficiency. Starting from a variational interpretation of diffusion models, in this work we quantify this trade-off, and suggest a new method to improve quality and efficiency of both training and sampling, by adopting smaller diffusion times. Indeed, we show how an auxiliary model can be used to bridge the gap between the ideal and the simulated forward dynamics, followed by a standard reverse diffusion process. Empirical results support our analysis; for image data, our method is competitive w.r.t. the state-of-the-art, according to standard sample quality metrics and log-likelihood.

Latent Consistency Models (LCMs) have achieved impressive performance in accelerating text-to-image generative tasks, producing high-quality images with minimal inference steps. LCMs are distilled from pre-trained latent diffusion models (LDMs), requiring only ~32 A100 GPU training hours. This report further extends LCMs' potential in two aspects: First, by applying LoRA distillation to Stable-Diffusion models including SD-V1.5, SSD-1B, and SDXL, we have expanded LCM's scope to larger models with significantly less memory consumption, achieving superior image generation quality. Second, we identify the LoRA parameters obtained through LCM distillation as a universal Stable-Diffusion acceleration module, named LCM-LoRA. LCM-LoRA can be directly plugged into various Stable-Diffusion fine-tuned models or LoRAs without training, thus representing a universally applicable accelerator for diverse image generation tasks. Compared with previous numerical PF-ODE solvers such as DDIM, DPM-Solver, LCM-LoRA can be viewed as a plug-in neural PF-ODE solver that possesses strong generalization abilities. Project page: https://github.com/luosiallen/latent-consistency-model.

Over the past decade, there has been tremendous progress in the domain of synthetic media generation. This is mainly due to the powerful methods based on generative adversarial networks (GANs). Very recently, diffusion probabilistic models, which are inspired by non-equilibrium thermodynamics, have taken the spotlight. In the realm of image generation, diffusion models (DMs) have exhibited remarkable proficiency in producing both realistic and heterogeneous imagery through their stochastic sampling procedure. This paper proposes a novel facial swapping module, termed as LDFaceNet (Latent Diffusion based Face Swapping Network), which is based on a guided latent diffusion model that utilizes facial segmentation and facial recognition modules for a conditioned denoising process. The model employs a unique loss function to offer directional guidance to the diffusion process. Notably, LDFaceNet can incorporate supplementary facial guidance for desired outcomes without any retraining. To the best of our knowledge, this represents the first application of the latent diffusion model in the face-swapping task without prior training. The results of this study demonstrate that the proposed method can generate extremely realistic and coherent images by leveraging the potential of the diffusion model for facial swapping, thereby yielding superior visual outcomes and greater diversity.

Latent diffusion models (LDMs) have made significant advancements in the field of image generation in recent years. One major advantage of LDMs is their ability to operate in a compressed latent space, allowing for more efficient training and deployment. However, despite these advantages, challenges with LDMs still remain. For example, it has been observed that LDMs often generate high-frequency details and complex compositions imperfectly. We hypothesize that one reason for these flaws is due to the fact that all pre- and post-training of LDMs are done in latent space, which is typically 8 times 8 lower spatial-resolution than the output images. To address this issue, we propose adding pixel-space supervision in the post-training process to better preserve high-frequency details. Experimentally, we show that adding a pixel-space objective significantly improves both supervised quality fine-tuning and preference-based post-training by a large margin on a state-of-the-art DiT transformer and U-Net diffusion models in both visual quality and visual flaw metrics, while maintaining the same text alignment quality.

Diffusion models are generative models that have recently demonstrated impressive performances in terms of sampling quality and density estimation in high dimensions. They rely on a forward continuous diffusion process and a backward continuous denoising process, which can be described by a time-dependent vector field and is used as a generative model. In the original formulation of the diffusion model, this vector field is assumed to be the score function (i.e. it is the gradient of the log-probability at a given time in the diffusion process). Curiously, on the practical side, most studies on diffusion models implement this vector field as a neural network function and do not constrain it be the gradient of some energy function (that is, most studies do not constrain the vector field to be conservative). Even though some studies investigated empirically whether such a constraint will lead to a performance gain, they lead to contradicting results and failed to provide analytical results. Here, we provide three analytical results regarding the extent of the modeling freedom of this vector field. {Firstly, we propose a novel decomposition of vector fields into a conservative component and an orthogonal component which satisfies a given (gauge) freedom. Secondly, from this orthogonal decomposition, we show that exact density estimation and exact sampling is achieved when the conservative component is exactly equals to the true score and therefore conservativity is neither necessary nor sufficient to obtain exact density estimation and exact sampling. Finally, we show that when it comes to inferring local information of the data manifold, constraining the vector field to be conservative is desirable.

Diffusion models are a class of probabilistic generative models that have been widely used as a prior for image processing tasks like text conditional generation and inpainting. We demonstrate that these models can be adapted to make predictions and provide uncertainty quantification for chaotic dynamical systems. In these applications, diffusion models can implicitly represent knowledge about outliers and extreme events; however, querying that knowledge through conditional sampling or measuring probabilities is surprisingly difficult. Existing methods for conditional sampling at inference time seek mainly to enforce the constraints, which is insufficient to match the statistics of the distribution or compute the probability of the chosen events. To achieve these ends, optimally one would use the conditional score function, but its computation is typically intractable. In this work, we develop a probabilistic approximation scheme for the conditional score function which provably converges to the true distribution as the noise level decreases. With this scheme we are able to sample conditionally on nonlinear userdefined events at inference time, and matches data statistics even when sampling from the tails of the distribution.

Generative models, especially diffusion models (DMs), have achieved promising results for generating feature-rich geometries and advancing foundational science problems such as molecule design. Inspired by the recent huge success of Stable (latent) Diffusion models, we propose a novel and principled method for 3D molecule generation named Geometric Latent Diffusion Models (GeoLDM). GeoLDM is the first latent DM model for the molecular geometry domain, composed of autoencoders encoding structures into continuous latent codes and DMs operating in the latent space. Our key innovation is that for modeling the 3D molecular geometries, we capture its critical roto-translational equivariance constraints by building a point-structured latent space with both invariant scalars and equivariant tensors. Extensive experiments demonstrate that GeoLDM can consistently achieve better performance on multiple molecule generation benchmarks, with up to 7\% improvement for the valid percentage of large biomolecules. Results also demonstrate GeoLDM's higher capacity for controllable generation thanks to the latent modeling. Code is provided at https://github.com/MinkaiXu/GeoLDM.

This article provides a mathematically rigorous introduction to denoising diffusion probabilistic models (DDPMs), sometimes also referred to as diffusion probabilistic models or diffusion models, for generative artificial intelligence. We provide a detailed basic mathematical framework for DDPMs and explain the main ideas behind training and generation procedures. In this overview article we also review selected extensions and improvements of the basic framework from the literature such as improved DDPMs, denoising diffusion implicit models, classifier-free diffusion guidance models, and latent diffusion models.

Denoising diffusion models, a class of generative models, have garnered immense interest lately in various deep-learning problems. A diffusion probabilistic model defines a forward diffusion stage where the input data is gradually perturbed over several steps by adding Gaussian noise and then learns to reverse the diffusion process to retrieve the desired noise-free data from noisy data samples. Diffusion models are widely appreciated for their strong mode coverage and quality of the generated samples despite their known computational burdens. Capitalizing on the advances in computer vision, the field of medical imaging has also observed a growing interest in diffusion models. To help the researcher navigate this profusion, this survey intends to provide a comprehensive overview of diffusion models in the discipline of medical image analysis. Specifically, we introduce the solid theoretical foundation and fundamental concepts behind diffusion models and the three generic diffusion modelling frameworks: diffusion probabilistic models, noise-conditioned score networks, and stochastic differential equations. Then, we provide a systematic taxonomy of diffusion models in the medical domain and propose a multi-perspective categorization based on their application, imaging modality, organ of interest, and algorithms. To this end, we cover extensive applications of diffusion models in the medical domain. Furthermore, we emphasize the practical use case of some selected approaches, and then we discuss the limitations of the diffusion models in the medical domain and propose several directions to fulfill the demands of this field. Finally, we gather the overviewed studies with their available open-source implementations at https://github.com/amirhossein-kz/Awesome-Diffusion-Models-in-Medical-Imaging.

Diffusion models are a class of generative models that learn to synthesize samples by inverting a diffusion process that gradually maps data into noise. While these models have enjoyed great success recently, a full theoretical understanding of their observed properties is still lacking, in particular, their weak sensitivity to the choice of noise family and the role of adequate scheduling of noise levels for good synthesis. By identifying a correspondence between diffusion models and a well-known paradigm in cognitive science known as serial reproduction, whereby human agents iteratively observe and reproduce stimuli from memory, we show how the aforementioned properties of diffusion models can be explained as a natural consequence of this correspondence. We then complement our theoretical analysis with simulations that exhibit these key features. Our work highlights how classic paradigms in cognitive science can shed light on state-of-the-art machine learning problems.

We introduce Diffusion World Model (DWM), a conditional diffusion model capable of predicting multistep future states and rewards concurrently. As opposed to traditional one-step dynamics models, DWM offers long-horizon predictions in a single forward pass, eliminating the need for recursive quires. We integrate DWM into model-based value estimation, where the short-term return is simulated by future trajectories sampled from DWM. In the context of offline reinforcement learning, DWM can be viewed as a conservative value regularization through generative modeling. Alternatively, it can be seen as a data source that enables offline Q-learning with synthetic data. Our experiments on the D4RL dataset confirm the robustness of DWM to long-horizon simulation. In terms of absolute performance, DWM significantly surpasses one-step dynamics models with a 44% performance gain, and achieves state-of-the-art performance.

Denoising Diffusion Models (DDMs) have become a popular tool for generating high-quality samples from complex data distributions. These models are able to capture sophisticated patterns and structures in the data, and can generate samples that are highly diverse and representative of the underlying distribution. However, one of the main limitations of diffusion models is the complexity of sample generation, since a large number of inference timesteps is required to faithfully capture the data distribution. In this paper, we present MMD-DDM, a novel method for fast sampling of diffusion models. Our approach is based on the idea of using the Maximum Mean Discrepancy (MMD) to finetune the learned distribution with a given budget of timesteps. This allows the finetuned model to significantly improve the speed-quality trade-off, by substantially increasing fidelity in inference regimes with few steps or, equivalently, by reducing the required number of steps to reach a target fidelity, thus paving the way for a more practical adoption of diffusion models in a wide range of applications. We evaluate our approach on unconditional image generation with extensive experiments across the CIFAR-10, CelebA, ImageNet and LSUN-Church datasets. Our findings show that the proposed method is able to produce high-quality samples in a fraction of the time required by widely-used diffusion models, and outperforms state-of-the-art techniques for accelerated sampling. Code is available at: https://github.com/diegovalsesia/MMD-DDM.

Unsupervised out-of-distribution detection (OOD) seeks to identify out-of-domain data by learning only from unlabeled in-domain data. We present a novel approach for this task - Lift, Map, Detect (LMD) - that leverages recent advancement in diffusion models. Diffusion models are one type of generative models. At their core, they learn an iterative denoising process that gradually maps a noisy image closer to their training manifolds. LMD leverages this intuition for OOD detection. Specifically, LMD lifts an image off its original manifold by corrupting it, and maps it towards the in-domain manifold with a diffusion model. For an out-of-domain image, the mapped image would have a large distance away from its original manifold, and LMD would identify it as OOD accordingly. We show through extensive experiments that LMD achieves competitive performance across a broad variety of datasets.

Diffusion models are powerful generative models that simulate the reverse of diffusion processes using score functions to synthesize data from noise. The sampling process of diffusion models can be interpreted as solving the reverse stochastic differential equation (SDE) or the ordinary differential equation (ODE) of the diffusion process, which often requires up to thousands of discretization steps to generate a single image. This has sparked a great interest in developing efficient integration techniques for reverse-S/ODEs. Here, we propose an orthogonal approach to accelerating score-based sampling: Denoising MCMC (DMCMC). DMCMC first uses MCMC to produce samples in the product space of data and variance (or diffusion time). Then, a reverse-S/ODE integrator is used to denoise the MCMC samples. Since MCMC traverses close to the data manifold, the computation cost of producing a clean sample for DMCMC is much less than that of producing a clean sample from noise. To verify the proposed concept, we show that Denoising Langevin Gibbs (DLG), an instance of DMCMC, successfully accelerates all six reverse-S/ODE integrators considered in this work on the tasks of CIFAR10 and CelebA-HQ-256 image generation. Notably, combined with integrators of Karras et al. (2022) and pre-trained score models of Song et al. (2021b), DLG achieves SOTA results. In the limited number of score function evaluation (NFE) settings on CIFAR10, we have 3.86 FID with approx 10 NFE and 2.63 FID with approx 20 NFE. On CelebA-HQ-256, we have 6.99 FID with approx 160 NFE, which beats the current best record of Kim et al. (2022) among score-based models, 7.16 FID with 4000 NFE. Code: https://github.com/1202kbs/DMCMC

Reversing a diffusion process by learning its score forms the heart of diffusion-based generative modeling and for estimating properties of scientific systems. The diffusion processes that are tractable center on linear processes with a Gaussian stationary distribution. This limits the kinds of models that can be built to those that target a Gaussian prior or more generally limits the kinds of problems that can be generically solved to those that have conditionally linear score functions. In this work, we introduce a family of tractable denoising score matching objectives, called local-DSM, built using local increments of the diffusion process. We show how local-DSM melded with Taylor expansions enables automated training and score estimation with nonlinear diffusion processes. To demonstrate these ideas, we use automated-DSM to train generative models using non-Gaussian priors on challenging low dimensional distributions and the CIFAR10 image dataset. Additionally, we use the automated-DSM to learn the scores for nonlinear processes studied in statistical physics.

Diffusion Models are popular generative modeling methods in various vision tasks, attracting significant attention. They can be considered a unique instance of self-supervised learning methods due to their independence from label annotation. This survey explores the interplay between diffusion models and representation learning. It provides an overview of diffusion models' essential aspects, including mathematical foundations, popular denoising network architectures, and guidance methods. Various approaches related to diffusion models and representation learning are detailed. These include frameworks that leverage representations learned from pre-trained diffusion models for subsequent recognition tasks and methods that utilize advancements in representation and self-supervised learning to enhance diffusion models. This survey aims to offer a comprehensive overview of the taxonomy between diffusion models and representation learning, identifying key areas of existing concerns and potential exploration. Github link: https://github.com/dongzhuoyao/Diffusion-Representation-Learning-Survey-Taxonomy

Diffusion models are a family of generative models that yield record-breaking performance in tasks such as image synthesis, video generation, and molecule design. Despite their capabilities, their efficiency, especially in the reverse denoising process, remains a challenge due to slow convergence rates and high computational costs. In this work, we introduce an approach that leverages continuous dynamical systems to design a novel denoising network for diffusion models that is more parameter-efficient, exhibits faster convergence, and demonstrates increased noise robustness. Experimenting with denoising probabilistic diffusion models, our framework operates with approximately a quarter of the parameters and 30% of the Floating Point Operations (FLOPs) compared to standard U-Nets in Denoising Diffusion Probabilistic Models (DDPMs). Furthermore, our model is up to 70% faster in inference than the baseline models when measured in equal conditions while converging to better quality solutions.

Denoising diffusion models (DDMs) have attracted attention for their exceptional generation quality and diversity. This success is largely attributed to the use of class- or text-conditional diffusion guidance methods, such as classifier and classifier-free guidance. In this paper, we present a more comprehensive perspective that goes beyond the traditional guidance methods. From this generalized perspective, we introduce novel condition- and training-free strategies to enhance the quality of generated images. As a simple solution, blur guidance improves the suitability of intermediate samples for their fine-scale information and structures, enabling diffusion models to generate higher quality samples with a moderate guidance scale. Improving upon this, Self-Attention Guidance (SAG) uses the intermediate self-attention maps of diffusion models to enhance their stability and efficacy. Specifically, SAG adversarially blurs only the regions that diffusion models attend to at each iteration and guides them accordingly. Our experimental results show that our SAG improves the performance of various diffusion models, including ADM, IDDPM, Stable Diffusion, and DiT. Moreover, combining SAG with conventional guidance methods leads to further improvement.

Diffusion models are powerful generative models that map noise to data using stochastic processes. However, for many applications such as image editing, the model input comes from a distribution that is not random noise. As such, diffusion models must rely on cumbersome methods like guidance or projected sampling to incorporate this information in the generative process. In our work, we propose Denoising Diffusion Bridge Models (DDBMs), a natural alternative to this paradigm based on diffusion bridges, a family of processes that interpolate between two paired distributions given as endpoints. Our method learns the score of the diffusion bridge from data and maps from one endpoint distribution to the other by solving a (stochastic) differential equation based on the learned score. Our method naturally unifies several classes of generative models, such as score-based diffusion models and OT-Flow-Matching, allowing us to adapt existing design and architectural choices to our more general problem. Empirically, we apply DDBMs to challenging image datasets in both pixel and latent space. On standard image translation problems, DDBMs achieve significant improvement over baseline methods, and, when we reduce the problem to image generation by setting the source distribution to random noise, DDBMs achieve comparable FID scores to state-of-the-art methods despite being built for a more general task.

We introduce Compartmentalized Diffusion Models (CDM), a method to train different diffusion models (or prompts) on distinct data sources and arbitrarily compose them at inference time. The individual models can be trained in isolation, at different times, and on different distributions and domains and can be later composed to achieve performance comparable to a paragon model trained on all data simultaneously. Furthermore, each model only contains information about the subset of the data it was exposed to during training, enabling several forms of training data protection. In particular, CDMs are the first method to enable both selective forgetting and continual learning for large-scale diffusion models, as well as allowing serving customized models based on the user's access rights. CDMs also allow determining the importance of a subset of the data in generating particular samples.

Diffusion models, which employ stochastic differential equations to sample images through integrals, have emerged as a dominant class of generative models. However, the rationality of the diffusion process itself receives limited attention, leaving the question of whether the problem is well-posed and well-conditioned. In this paper, we uncover a vexing propensity of diffusion models: they frequently exhibit the infinite Lipschitz near the zero point of timesteps. This poses a threat to the stability and accuracy of the diffusion process, which relies on integral operations. We provide a comprehensive evaluation of the issue from both theoretical and empirical perspectives. To address this challenge, we propose a novel approach, dubbed E-TSDM, which eliminates the Lipschitz singularity of the diffusion model near zero. Remarkably, our technique yields a substantial improvement in performance, e.g., on the high-resolution FFHQ dataset (256times256). Moreover, as a byproduct of our method, we manage to achieve a dramatic reduction in the Frechet Inception Distance of other acceleration methods relying on network Lipschitz, including DDIM and DPM-Solver, by over 33%. We conduct extensive experiments on diverse datasets to validate our theory and method. Our work not only advances the understanding of the general diffusion process, but also provides insights for the design of diffusion models.

Known for their impressive performance in generative modeling, diffusion models are attractive candidates for density-based anomaly detection. This paper investigates different variations of diffusion modeling for unsupervised and semi-supervised anomaly detection. In particular, we find that Denoising Diffusion Probability Models (DDPM) are performant on anomaly detection benchmarks yet computationally expensive. By simplifying DDPM in application to anomaly detection, we are naturally led to an alternative approach called Diffusion Time Estimation (DTE). DTE estimates the distribution over diffusion time for a given input and uses the mode or mean of this distribution as the anomaly score. We derive an analytical form for this density and leverage a deep neural network to improve inference efficiency. Through empirical evaluations on the ADBench benchmark, we demonstrate that all diffusion-based anomaly detection methods perform competitively for both semi-supervised and unsupervised settings. Notably, DTE achieves orders of magnitude faster inference time than DDPM, while outperforming it on this benchmark. These results establish diffusion-based anomaly detection as a scalable alternative to traditional methods and recent deep-learning techniques for standard unsupervised and semi-supervised anomaly detection settings.

Diffusion Language Models (DLMs) have emerged as a promising new paradigm for text generative modeling, potentially addressing limitations of autoregressive (AR) models. However, current DLMs have been studied at a smaller scale compared to their AR counterparts and lack fair comparison on language modeling benchmarks. Additionally, training diffusion models from scratch at scale remains challenging. Given the prevalence of open-source AR language models, we propose adapting these models to build text diffusion models. We demonstrate connections between AR and diffusion modeling objectives and introduce a simple continual pre-training approach for training diffusion models. Through systematic evaluation on language modeling, reasoning, and commonsense benchmarks, we show that we can convert AR models ranging from 127M to 7B parameters (GPT2 and LLaMA) into diffusion models DiffuGPT and DiffuLLaMA, using less than 200B tokens for training. Our experimental results reveal that these models outperform earlier DLMs and are competitive with their AR counterparts. We release a suite of DLMs (with 127M, 355M, and 7B parameters) capable of generating fluent text, performing in-context learning, filling in the middle without prompt re-ordering, and following instructions https://github.com/HKUNLP/DiffuLLaMA.

Diffusion models (DMs) have revolutionized generative learning. They utilize a diffusion process to encode data into a simple Gaussian distribution. However, encoding a complex, potentially multimodal data distribution into a single continuous Gaussian distribution arguably represents an unnecessarily challenging learning problem. We propose Discrete-Continuous Latent Variable Diffusion Models (DisCo-Diff) to simplify this task by introducing complementary discrete latent variables. We augment DMs with learnable discrete latents, inferred with an encoder, and train DM and encoder end-to-end. DisCo-Diff does not rely on pre-trained networks, making the framework universally applicable. The discrete latents significantly simplify learning the DM's complex noise-to-data mapping by reducing the curvature of the DM's generative ODE. An additional autoregressive transformer models the distribution of the discrete latents, a simple step because DisCo-Diff requires only few discrete variables with small codebooks. We validate DisCo-Diff on toy data, several image synthesis tasks as well as molecular docking, and find that introducing discrete latents consistently improves model performance. For example, DisCo-Diff achieves state-of-the-art FID scores on class-conditioned ImageNet-64/128 datasets with ODE sampler.

Recent work in Video Frame Interpolation (VFI) tries to formulate VFI as a diffusion-based conditional image generation problem, synthesizing the intermediate frame given a random noise and neighboring frames. Due to the relatively high resolution of videos, Latent Diffusion Models (LDMs) are employed as the conditional generation model, where the autoencoder compresses images into latent representations for diffusion and then reconstructs images from these latent representations. Such a formulation poses a crucial challenge: VFI expects that the output is deterministically equal to the ground truth intermediate frame, but LDMs randomly generate a diverse set of different images when the model runs multiple times. The reason for the diverse generation is that the cumulative variance (variance accumulated at each step of generation) of generated latent representations in LDMs is large. This makes the sampling trajectory random, resulting in diverse rather than deterministic generations. To address this problem, we propose our unique solution: Frame Interpolation with Consecutive Brownian Bridge Diffusion. Specifically, we propose consecutive Brownian Bridge diffusion that takes a deterministic initial value as input, resulting in a much smaller cumulative variance of generated latent representations. Our experiments suggest that our method can improve together with the improvement of the autoencoder and achieve state-of-the-art performance in VFI, leaving strong potential for further enhancement.

Diffusion models, a powerful and universal generative AI technology, have achieved tremendous success in computer vision, audio, reinforcement learning, and computational biology. In these applications, diffusion models provide flexible high-dimensional data modeling, and act as a sampler for generating new samples under active guidance towards task-desired properties. Despite the significant empirical success, theory of diffusion models is very limited, potentially slowing down principled methodological innovations for further harnessing and improving diffusion models. In this paper, we review emerging applications of diffusion models, understanding their sample generation under various controls. Next, we overview the existing theories of diffusion models, covering their statistical properties and sampling capabilities. We adopt a progressive routine, beginning with unconditional diffusion models and connecting to conditional counterparts. Further, we review a new avenue in high-dimensional structured optimization through conditional diffusion models, where searching for solutions is reformulated as a conditional sampling problem and solved by diffusion models. Lastly, we discuss future directions about diffusion models. The purpose of this paper is to provide a well-rounded theoretical exposure for stimulating forward-looking theories and methods of diffusion models.

Diffusion models (DMs) represent state-of-the-art generative models for continuous inputs. DMs work by constructing a Stochastic Differential Equation (SDE) in the input space (ie, position space), and using a neural network to reverse it. In this work, we introduce a novel generative modeling framework grounded in phase space dynamics, where a phase space is defined as {an augmented space encompassing both position and velocity.} Leveraging insights from Stochastic Optimal Control, we construct a path measure in the phase space that enables efficient sampling. {In contrast to DMs, our framework demonstrates the capability to generate realistic data points at an early stage of dynamics propagation.} This early prediction sets the stage for efficient data generation by leveraging additional velocity information along the trajectory. On standard image generation benchmarks, our model yields favorable performance over baselines in the regime of small Number of Function Evaluations (NFEs). Furthermore, our approach rivals the performance of diffusion models equipped with efficient sampling techniques, underscoring its potential as a new tool generative modeling.

Object counting methods typically rely on manually annotated datasets. The cost of creating such datasets has restricted the versatility of these networks to count objects from specific classes (such as humans or penguins), and counting objects from diverse categories remains a challenge. The availability of robust text-to-image latent diffusion models (LDMs) raises the question of whether these models can be utilized to generate counting datasets. However, LDMs struggle to create images with an exact number of objects based solely on text prompts but they can be used to offer a dependable sorting signal by adding and removing objects within an image. Leveraging this data, we initially introduce an unsupervised sorting methodology to learn object-related features that are subsequently refined and anchored for counting purposes using counting data generated by LDMs. Further, we present a density classifier-guided method for dividing an image into patches containing objects that can be reliably counted. Consequently, we can generate counting data for any type of object and count them in an unsupervised manner. Our approach outperforms other unsupervised and few-shot alternatives and is not restricted to specific object classes for which counting data is available. Code to be released upon acceptance.

Digital Surface Models (DSM) offer a wealth of height information for understanding the Earth's surface as well as monitoring the existence or change in natural and man-made structures. Classical height estimation requires multi-view geospatial imagery or LiDAR point clouds which can be expensive to acquire. Single-view height estimation using neural network based models shows promise however it can struggle with reconstructing high resolution features. The latest advancements in diffusion models for high resolution image synthesis and editing have yet to be utilized for remote sensing imagery, particularly height estimation. Our approach involves training a generative diffusion model to learn the joint distribution of optical and DSM images across both domains as a Markov chain. This is accomplished by minimizing a denoising score matching objective while being conditioned on the source image to generate realistic high resolution 3D surfaces. In this paper we experiment with conditional denoising diffusion probabilistic models (DDPM) for height estimation from a single remotely sensed image and show promising results on the Vaihingen benchmark dataset.

Diffusion models (DMs) have established themselves as the state-of-the-art generative modeling approach in the visual domain and beyond. A crucial drawback of DMs is their slow sampling speed, relying on many sequential function evaluations through large neural networks. Sampling from DMs can be seen as solving a differential equation through a discretized set of noise levels known as the sampling schedule. While past works primarily focused on deriving efficient solvers, little attention has been given to finding optimal sampling schedules, and the entire literature relies on hand-crafted heuristics. In this work, for the first time, we propose a general and principled approach to optimizing the sampling schedules of DMs for high-quality outputs, called Align Your Steps. We leverage methods from stochastic calculus and find optimal schedules specific to different solvers, trained DMs and datasets. We evaluate our novel approach on several image, video as well as 2D toy data synthesis benchmarks, using a variety of different samplers, and observe that our optimized schedules outperform previous hand-crafted schedules in almost all experiments. Our method demonstrates the untapped potential of sampling schedule optimization, especially in the few-step synthesis regime.

Diffusion models have emerged as a powerful new family of deep generative models with record-breaking performance in many applications, including image synthesis, video generation, and molecule design. In this survey, we provide an overview of the rapidly expanding body of work on diffusion models, categorizing the research into three key areas: efficient sampling, improved likelihood estimation, and handling data with special structures. We also discuss the potential for combining diffusion models with other generative models for enhanced results. We further review the wide-ranging applications of diffusion models in fields spanning from computer vision, natural language generation, temporal data modeling, to interdisciplinary applications in other scientific disciplines. This survey aims to provide a contextualized, in-depth look at the state of diffusion models, identifying the key areas of focus and pointing to potential areas for further exploration. Github: https://github.com/YangLing0818/Diffusion-Models-Papers-Survey-Taxonomy.

The Stable Diffusion Model (SDM) is a prevalent and effective model for text-to-image (T2I) and image-to-image (I2I) generation. Despite various attempts at sampler optimization, model distillation, and network quantification, these approaches typically maintain the original network architecture. The extensive parameter scale and substantial computational demands have limited research into adjusting the model architecture. This study focuses on reducing redundant computation in SDM and optimizes the model through both tuning and tuning-free methods. 1) For the tuning method, we design a model assembly strategy to reconstruct a lightweight model while preserving performance through distillation. Second, to mitigate performance loss due to pruning, we incorporate multi-expert conditional convolution (ME-CondConv) into compressed UNets to enhance network performance by increasing capacity without sacrificing speed. Third, we validate the effectiveness of the multi-UNet switching method for improving network speed. 2) For the tuning-free method, we propose a feature inheritance strategy to accelerate inference by skipping local computations at the block, layer, or unit level within the network structure. We also examine multiple sampling modes for feature inheritance at the time-step level. Experiments demonstrate that both the proposed tuning and the tuning-free methods can improve the speed and performance of the SDM. The lightweight model reconstructed by the model assembly strategy increases generation speed by 22.4%, while the feature inheritance strategy enhances the SDM generation speed by 40.0%.

Diffusion models that are based on iterative denoising have been recently proposed and leveraged in various generation tasks like image generation. Whereas, as a way inherently built for continuous data, existing diffusion models still have some limitations in modeling discrete data, e.g., languages. For example, the generally used Gaussian noise can not handle the discrete corruption well, and the objectives in continuous spaces fail to be stable for textual data in the diffusion process especially when the dimension is high. To alleviate these issues, we introduce a novel diffusion model for language modeling, Masked-Diffuse LM, with lower training cost and better performances, inspired by linguistic features in languages. Specifically, we design a linguistic-informed forward process which adds corruptions to the text through strategically soft-masking to better noise the textual data. Also, we directly predict the categorical distribution with cross-entropy loss function in every diffusion step to connect the continuous space and discrete space in a more efficient and straightforward way. Through experiments on 5 controlled generation tasks, we demonstrate that our Masked-Diffuse LM can achieve better generation quality than the state-of-the-art diffusion models with better efficiency.

Denoising diffusion probabilistic models (DDPMs) (Ho et al. 2020) have shown impressive results on image and waveform generation in continuous state spaces. Here, we introduce Discrete Denoising Diffusion Probabilistic Models (D3PMs), diffusion-like generative models for discrete data that generalize the multinomial diffusion model of Hoogeboom et al. 2021, by going beyond corruption processes with uniform transition probabilities. This includes corruption with transition matrices that mimic Gaussian kernels in continuous space, matrices based on nearest neighbors in embedding space, and matrices that introduce absorbing states. The third allows us to draw a connection between diffusion models and autoregressive and mask-based generative models. We show that the choice of transition matrix is an important design decision that leads to improved results in image and text domains. We also introduce a new loss function that combines the variational lower bound with an auxiliary cross entropy loss. For text, this model class achieves strong results on character-level text generation while scaling to large vocabularies on LM1B. On the image dataset CIFAR-10, our models approach the sample quality and exceed the log-likelihood of the continuous-space DDPM model.

Advances in latent diffusion models (LDMs) have revolutionized high-resolution image generation, but the design space of the autoencoder that is central to these systems remains underexplored. In this paper, we introduce LiteVAE, a family of autoencoders for LDMs that leverage the 2D discrete wavelet transform to enhance scalability and computational efficiency over standard variational autoencoders (VAEs) with no sacrifice in output quality. We also investigate the training methodologies and the decoder architecture of LiteVAE and propose several enhancements that improve the training dynamics and reconstruction quality. Our base LiteVAE model matches the quality of the established VAEs in current LDMs with a six-fold reduction in encoder parameters, leading to faster training and lower GPU memory requirements, while our larger model outperforms VAEs of comparable complexity across all evaluated metrics (rFID, LPIPS, PSNR, and SSIM).

We present a dynamic model in which the weights are conditioned on an input sample x and are learned to match those that would be obtained by finetuning a base model on x and its label y. This mapping between an input sample and network weights is approximated by a denoising diffusion model. The diffusion model we employ focuses on modifying a single layer of the base model and is conditioned on the input, activations, and output of this layer. Since the diffusion model is stochastic in nature, multiple initializations generate different networks, forming an ensemble, which leads to further improvements. Our experiments demonstrate the wide applicability of the method for image classification, 3D reconstruction, tabular data, speech separation, and natural language processing. Our code is available at https://github.com/ShaharLutatiPersonal/OCD

Diffusion models are a powerful class of generative models which simulate stochastic differential equations (SDEs) to generate data from noise. While diffusion models have achieved remarkable progress, they have limitations in unpaired image-to-image (I2I) translation tasks due to the Gaussian prior assumption. Schr\"{o}dinger Bridge (SB), which learns an SDE to translate between two arbitrary distributions, have risen as an attractive solution to this problem. Yet, to our best knowledge, none of SB models so far have been successful at unpaired translation between high-resolution images. In this work, we propose Unpaired Neural Schr\"{o}dinger Bridge (UNSB), which expresses the SB problem as a sequence of adversarial learning problems. This allows us to incorporate advanced discriminators and regularization to learn a SB between unpaired data. We show that UNSB is scalable and successfully solves various unpaired I2I translation tasks. Code: https://github.com/cyclomon/UNSB

Distilling large latent diffusion models (LDMs) into ones that are fast to sample from is attracting growing research interest. However, the majority of existing methods face a dilemma where they either (i) depend on multiple individual distilled models for different sampling budgets, or (ii) sacrifice generation quality with limited (e.g., 2-4) and/or moderate (e.g., 5-8) sampling steps. To address these, we extend the recent multistep consistency distillation (MCD) strategy to representative LDMs, establishing the Multistep Latent Consistency Models (MLCMs) approach for low-cost high-quality image synthesis. MLCM serves as a unified model for various sampling steps due to the promise of MCD. We further augment MCD with a progressive training strategy to strengthen inter-segment consistency to boost the quality of few-step generations. We take the states from the sampling trajectories of the teacher model as training data for MLCMs to lift the requirements for high-quality training datasets and to bridge the gap between the training and inference of the distilled model. MLCM is compatible with preference learning strategies for further improvement of visual quality and aesthetic appeal. Empirically, MLCM can generate high-quality, delightful images with only 2-8 sampling steps. On the MSCOCO-2017 5K benchmark, MLCM distilled from SDXL gets a CLIP Score of 33.30, Aesthetic Score of 6.19, and Image Reward of 1.20 with only 4 steps, substantially surpassing 4-step LCM [23], 8-step SDXL-Lightning [17], and 8-step HyperSD [33]. We also demonstrate the versatility of MLCMs in applications including controllable generation, image style transfer, and Chinese-to-image generation.

Diffusion models have recently emerged as powerful generative priors for solving inverse problems. However, training diffusion models in the pixel space are both data-intensive and computationally demanding, which restricts their applicability as priors for high-dimensional real-world data such as medical images. Latent diffusion models, which operate in a much lower-dimensional space, offer a solution to these challenges. However, incorporating latent diffusion models to solve inverse problems remains a challenging problem due to the nonlinearity of the encoder and decoder. To address these issues, we propose ReSample, an algorithm that can solve general inverse problems with pre-trained latent diffusion models. Our algorithm incorporates data consistency by solving an optimization problem during the reverse sampling process, a concept that we term as hard data consistency. Upon solving this optimization problem, we propose a novel resampling scheme to map the measurement-consistent sample back onto the noisy data manifold and theoretically demonstrate its benefits. Lastly, we apply our algorithm to solve a wide range of linear and nonlinear inverse problems in both natural and medical images, demonstrating that our approach outperforms existing state-of-the-art approaches, including those based on pixel-space diffusion models.

Diffusion models have achieved unprecedented performance in generative modeling. The commonly-adopted formulation of the latent code of diffusion models is a sequence of gradually denoised samples, as opposed to the simpler (e.g., Gaussian) latent space of GANs, VAEs, and normalizing flows. This paper provides an alternative, Gaussian formulation of the latent space of various diffusion models, as well as an invertible DPM-Encoder that maps images into the latent space. While our formulation is purely based on the definition of diffusion models, we demonstrate several intriguing consequences. (1) Empirically, we observe that a common latent space emerges from two diffusion models trained independently on related domains. In light of this finding, we propose CycleDiffusion, which uses DPM-Encoder for unpaired image-to-image translation. Furthermore, applying CycleDiffusion to text-to-image diffusion models, we show that large-scale text-to-image diffusion models can be used as zero-shot image-to-image editors. (2) One can guide pre-trained diffusion models and GANs by controlling the latent codes in a unified, plug-and-play formulation based on energy-based models. Using the CLIP model and a face recognition model as guidance, we demonstrate that diffusion models have better coverage of low-density sub-populations and individuals than GANs. The code is publicly available at https://github.com/ChenWu98/cycle-diffusion.

The consistency model (CM) has recently made significant progress in accelerating the generation of diffusion models. However, its application to high-resolution, text-conditioned image generation in the latent space (a.k.a., LCM) remains unsatisfactory. In this paper, we identify three key flaws in the current design of LCM. We investigate the reasons behind these limitations and propose the Phased Consistency Model (PCM), which generalizes the design space and addresses all identified limitations. Our evaluations demonstrate that PCM significantly outperforms LCM across 1--16 step generation settings. While PCM is specifically designed for multi-step refinement, it achieves even superior or comparable 1-step generation results to previously state-of-the-art specifically designed 1-step methods. Furthermore, we show that PCM's methodology is versatile and applicable to video generation, enabling us to train the state-of-the-art few-step text-to-video generator. More details are available at https://g-u-n.github.io/projects/pcm/.

Denoising diffusion models are a powerful type of generative models used to capture complex distributions of real-world signals. However, their applicability is limited to scenarios where training samples are readily available, which is not always the case in real-world applications. For example, in inverse graphics, the goal is to generate samples from a distribution of 3D scenes that align with a given image, but ground-truth 3D scenes are unavailable and only 2D images are accessible. To address this limitation, we propose a novel class of denoising diffusion probabilistic models that learn to sample from distributions of signals that are never directly observed. Instead, these signals are measured indirectly through a known differentiable forward model, which produces partial observations of the unknown signal. Our approach involves integrating the forward model directly into the denoising process. This integration effectively connects the generative modeling of observations with the generative modeling of the underlying signals, allowing for end-to-end training of a conditional generative model over signals. During inference, our approach enables sampling from the distribution of underlying signals that are consistent with a given partial observation. We demonstrate the effectiveness of our method on three challenging computer vision tasks. For instance, in the context of inverse graphics, our model enables direct sampling from the distribution of 3D scenes that align with a single 2D input image.

The intensive computational burden of Stable Diffusion (SD) for text-to-image generation poses a significant hurdle for its practical application. To tackle this challenge, recent research focuses on methods to reduce sampling steps, such as Latent Consistency Model (LCM), and on employing architectural optimizations, including pruning and knowledge distillation. Diverging from existing approaches, we uniquely start with a compact SD variant, BK-SDM. We observe that directly applying LCM to BK-SDM with commonly used crawled datasets yields unsatisfactory results. It leads us to develop two strategies: (1) leveraging high-quality image-text pairs from leading generative models and (2) designing an advanced distillation process tailored for LCM. Through our thorough exploration of quantization, profiling, and on-device deployment, we achieve rapid generation of photo-realistic, text-aligned images in just two steps, with latency under one second on resource-limited edge devices.

Diffusion models (DMs) have recently been introduced in image deblurring and exhibited promising performance, particularly in terms of details reconstruction. However, the diffusion model requires a large number of inference iterations to recover the clean image from pure Gaussian noise, which consumes massive computational resources. Moreover, the distribution synthesized by the diffusion model is often misaligned with the target results, leading to restrictions in distortion-based metrics. To address the above issues, we propose the Hierarchical Integration Diffusion Model (HI-Diff), for realistic image deblurring. Specifically, we perform the DM in a highly compacted latent space to generate the prior feature for the deblurring process. The deblurring process is implemented by a regression-based method to obtain better distortion accuracy. Meanwhile, the highly compact latent space ensures the efficiency of the DM. Furthermore, we design the hierarchical integration module to fuse the prior into the regression-based model from multiple scales, enabling better generalization in complex blurry scenarios. Comprehensive experiments on synthetic and real-world blur datasets demonstrate that our HI-Diff outperforms state-of-the-art methods. Code and trained models are available at https://github.com/zhengchen1999/HI-Diff.

Diffusion models, as a novel generative paradigm, have achieved remarkable success in various image generation tasks such as image inpainting, image-to-text translation, and video generation. Graph generation is a crucial computational task on graphs with numerous real-world applications. It aims to learn the distribution of given graphs and then generate new graphs. Given the great success of diffusion models in image generation, increasing efforts have been made to leverage these techniques to advance graph generation in recent years. In this paper, we first provide a comprehensive overview of generative diffusion models on graphs, In particular, we review representative algorithms for three variants of graph diffusion models, i.e., Score Matching with Langevin Dynamics (SMLD), Denoising Diffusion Probabilistic Model (DDPM), and Score-based Generative Model (SGM). Then, we summarize the major applications of generative diffusion models on graphs with a specific focus on molecule and protein modeling. Finally, we discuss promising directions in generative diffusion models on graph-structured data. For this survey, we also created a GitHub project website by collecting the supporting resources for generative diffusion models on graphs, at the link: https://github.com/ChengyiLIU-cs/Generative-Diffusion-Models-on-Graphs

Diffusion models have emerged as a promising alternative to autoregressive models in modeling discrete categorical data. Yet diffusion models that directly work on discrete data space do not fully exploit the power of iterative refinement, as the signals are lost during the transition between discrete states. Existing continuous diffusion models for discrete data have limited performance compared to discrete approaches, and the unclear link between them restricts the development of diffusion models for discrete data. In this work, we propose a continuous diffusion model for language modeling that incorporates the geometry of the underlying categorical distribution. We establish a connection between the discrete diffusion and continuous flow on the statistical manifold, and building on the analogy, we introduce a simple design for the diffusion process that generalizes previous discrete diffusion models. We further propose a simulation-free training framework based on radial symmetry and a simple technique to address the high dimensionality of the manifold. Comprehensive experiments on language modeling benchmarks and other modalities show that our method outperforms existing discrete diffusion models and approaches the performance of autoregressive models. Codes available at https://github.com/harryjo97/RDLM{https://github.com/harryjo97/RDLM}.

Diffusion models may be viewed as hierarchical variational autoencoders (VAEs) with two improvements: parameter sharing for the conditional distributions in the generative process and efficient computation of the loss as independent terms over the hierarchy. We consider two changes to the diffusion model that retain these advantages while adding flexibility to the model. Firstly, we introduce a data- and depth-dependent mean function in the diffusion process, which leads to a modified diffusion loss. Our proposed framework, DiffEnc, achieves a statistically significant improvement in likelihood on CIFAR-10. Secondly, we let the ratio of the noise variance of the reverse encoder process and the generative process be a free weight parameter rather than being fixed to 1. This leads to theoretical insights: For a finite depth hierarchy, the evidence lower bound (ELBO) can be used as an objective for a weighted diffusion loss approach and for optimizing the noise schedule specifically for inference. For the infinite-depth hierarchy, on the other hand, the weight parameter has to be 1 to have a well-defined ELBO.

In the burgeoning field of natural language processing, Neural Topic Models (NTMs) and Large Language Models (LLMs) have emerged as areas of significant research interest. Despite this, NTMs primarily utilize contextual embeddings from LLMs, which are not optimal for clustering or capable for topic generation. Our study addresses this gap by introducing a novel framework named Diffusion-Enhanced Topic Modeling using Encoder-Decoder-based LLMs (DeTiME). DeTiME leverages ncoder-Decoder-based LLMs to produce highly clusterable embeddings that could generate topics that exhibit both superior clusterability and enhanced semantic coherence compared to existing methods. Additionally, by exploiting the power of diffusion, our framework also provides the capability to generate content relevant to the identified topics. This dual functionality allows users to efficiently produce highly clustered topics and related content simultaneously. DeTiME's potential extends to generating clustered embeddings as well. Notably, our proposed framework proves to be efficient to train and exhibits high adaptability, demonstrating its potential for a wide array of applications.

Recent years have witnessed significant progress in developing efficient training and fast sampling approaches for diffusion models. A recent remarkable advancement is the use of stochastic differential equations (SDEs) to describe data perturbation and generative modeling in a unified mathematical framework. In this paper, we reveal several intriguing geometric structures of diffusion models and contribute a simple yet powerful interpretation to their sampling dynamics. Through carefully inspecting a popular variance-exploding SDE and its marginal-preserving ordinary differential equation (ODE) for sampling, we discover that the data distribution and the noise distribution are smoothly connected with an explicit, quasi-linear sampling trajectory, and another implicit denoising trajectory, which even converges faster in terms of visual quality. We also establish a theoretical relationship between the optimal ODE-based sampling and the classic mean-shift (mode-seeking) algorithm, with which we can characterize the asymptotic behavior of diffusion models and identify the score deviation. These new geometric observations enable us to improve previous sampling algorithms, re-examine latent interpolation, as well as re-explain the working principles of distillation-based fast sampling techniques.

With the emergence of diffusion models as the frontline of generative models, many researchers have proposed molecule generation techniques using conditional diffusion models. However, due to the fundamental nature of a molecule, which carries highly entangled correlations within a small number of atoms and bonds, it becomes difficult for a model to connect raw data with the conditions when the conditions become more complex as natural language. To address this, here we present a novel latent diffusion model dubbed LDMol, which enables a natural text-conditioned molecule generation. Specifically, LDMol is composed of three building blocks: a molecule encoder that produces a chemically informative feature space, a natural language-conditioned latent diffusion model using a Diffusion Transformer (DiT), and an autoregressive decoder for molecule re. In particular, recognizing that multiple SMILES notations can represent the same molecule, we employ a contrastive learning strategy to extract the chemical informative feature space. LDMol not only beats the existing baselines on the text-to-molecule generation benchmark but is also capable of zero-shot inference with unseen scenarios. Furthermore, we show that LDMol can be applied to downstream tasks such as molecule-to-text retrieval and text-driven molecule editing, demonstrating its versatility as a diffusion model.

Protein design with desirable properties has been a significant challenge for many decades. Generative artificial intelligence is a promising approach and has achieved great success in various protein generation tasks. Notably, diffusion models stand out for their robust mathematical foundations and impressive generative capabilities, offering unique advantages in certain applications such as protein design. In this review, we first give the definition and characteristics of diffusion models and then focus on two strategies: Denoising Diffusion Probabilistic Models and Score-based Generative Models, where DDPM is the discrete form of SGM. Furthermore, we discuss their applications in protein design, peptide generation, drug discovery, and protein-ligand interaction. Finally, we outline the future perspectives of diffusion models to advance autonomous protein design and engineering. The E(3) group consists of all rotations, reflections, and translations in three-dimensions. The equivariance on the E(3) group can keep the physical stability of the frame of each amino acid as much as possible, and we reflect on how to keep the diffusion model E(3) equivariant for protein generation.

Single-view novel view synthesis, the task of generating images from new viewpoints based on a single reference image, is an important but challenging task in computer vision. Recently, Denoising Diffusion Probabilistic Model (DDPM) has become popular in this area due to its strong ability to generate high-fidelity images. However, current diffusion-based methods directly rely on camera pose matrices as viewing conditions, globally and implicitly introducing 3D constraints. These methods may suffer from inconsistency among generated images from different perspectives, especially in regions with intricate textures and structures. In this work, we present Light Field Diffusion (LFD), a conditional diffusion-based model for single-view novel view synthesis. Unlike previous methods that employ camera pose matrices, LFD transforms the camera view information into light field encoding and combines it with the reference image. This design introduces local pixel-wise constraints within the diffusion models, thereby encouraging better multi-view consistency. Experiments on several datasets show that our LFD can efficiently generate high-fidelity images and maintain better 3D consistency even in intricate regions. Our method can generate images with higher quality than NeRF-based models, and we obtain sample quality similar to other diffusion-based models but with only one-third of the model size.

Denoising diffusion probabilistic models are currently becoming the leading paradigm of generative modeling for many important data modalities. Being the most prevalent in the computer vision community, diffusion models have also recently gained some attention in other domains, including speech, NLP, and graph-like data. In this work, we investigate if the framework of diffusion models can be advantageous for general tabular problems, where datapoints are typically represented by vectors of heterogeneous features. The inherent heterogeneity of tabular data makes it quite challenging for accurate modeling, since the individual features can be of completely different nature, i.e., some of them can be continuous and some of them can be discrete. To address such data types, we introduce TabDDPM -- a diffusion model that can be universally applied to any tabular dataset and handles any type of feature. We extensively evaluate TabDDPM on a wide set of benchmarks and demonstrate its superiority over existing GAN/VAE alternatives, which is consistent with the advantage of diffusion models in other fields. Additionally, we show that TabDDPM is eligible for privacy-oriented setups, where the original datapoints cannot be publicly shared.

Diffusion models have shown remarkable performance on many generative tasks. Despite recent success, most diffusion models are restricted in that they only allow linear transformation of the data distribution. In contrast, broader family of transformations can potentially help train generative distributions more efficiently, simplifying the reverse process and closing the gap between the true negative log-likelihood and the variational approximation. In this paper, we present Neural Diffusion Models (NDMs), a generalization of conventional diffusion models that enables defining and learning time-dependent non-linear transformations of data. We show how to optimise NDMs using a variational bound in a simulation-free setting. Moreover, we derive a time-continuous formulation of NDMs, which allows fast and reliable inference using off-the-shelf numerical ODE and SDE solvers. Finally, we demonstrate the utility of NDMs with learnable transformations through experiments on standard image generation benchmarks, including CIFAR-10, downsampled versions of ImageNet and CelebA-HQ. NDMs outperform conventional diffusion models in terms of likelihood and produce high-quality samples.

Current diffusion-based image restoration methods feed degraded input images as conditions into the noise estimation network. However, interpreting this diffusion process is challenging since it essentially generates the target image from the noise. To establish a unified and more interpretable model for image generation and restoration, we propose residual denoising diffusion models (RDDM). In contrast to existing diffusion models (e.g., DDPM or DDIM) that focus solely on noise estimation, our RDDM predicts residuals to represent directional diffusion from the target domain to the input domain, while concurrently estimating noise to account for random perturbations in the diffusion process. The introduction of residuals allows us to redefine the forward diffusion process, wherein the target image progressively diffuses into a purely noisy image or a noise-carrying input image, thus unifying image generation and restoration. We demonstrate that our sampling process is consistent with that of DDPM and DDIM through coefficient transformation, and propose a partially path-independent generation process to better understand the reverse process. Notably, with native support for conditional inputs, our RDDM enables a generic UNet, trained with only an ell _1 loss and a batch size of 1, to compete with state-of-the-art image restoration methods. We provide code and pre-trained models to encourage further exploration, application, and development of our innovative framework (https://github.com/nachifur/RDDM).

Denoising diffusion probabilistic models (DDPM) are a class of generative models which have recently been shown to produce excellent samples. We show that with a few simple modifications, DDPMs can also achieve competitive log-likelihoods while maintaining high sample quality. Additionally, we find that learning variances of the reverse diffusion process allows sampling with an order of magnitude fewer forward passes with a negligible difference in sample quality, which is important for the practical deployment of these models. We additionally use precision and recall to compare how well DDPMs and GANs cover the target distribution. Finally, we show that the sample quality and likelihood of these models scale smoothly with model capacity and training compute, making them easily scalable. We release our code at https://github.com/openai/improved-diffusion

Diffusion models are emerging expressive generative models, in which a large number of time steps (inference steps) are required for a single image generation. To accelerate such tedious process, reducing steps uniformly is considered as an undisputed principle of diffusion models. We consider that such a uniform assumption is not the optimal solution in practice; i.e., we can find different optimal time steps for different models. Therefore, we propose to search the optimal time steps sequence and compressed model architecture in a unified framework to achieve effective image generation for diffusion models without any further training. Specifically, we first design a unified search space that consists of all possible time steps and various architectures. Then, a two stage evolutionary algorithm is introduced to find the optimal solution in the designed search space. To further accelerate the search process, we employ FID score between generated and real samples to estimate the performance of the sampled examples. As a result, the proposed method is (i).training-free, obtaining the optimal time steps and model architecture without any training process; (ii). orthogonal to most advanced diffusion samplers and can be integrated to gain better sample quality. (iii). generalized, where the searched time steps and architectures can be directly applied on different diffusion models with the same guidance scale. Experimental results show that our method achieves excellent performance by using only a few time steps, e.g. 17.86 FID score on ImageNet 64 times 64 with only four steps, compared to 138.66 with DDIM. The code is available at https://github.com/lilijiangg/AutoDiffusion.

Diffusion models achieved great success in image synthesis, but still face challenges in high-resolution generation. Through the lens of discrete cosine transformation, we find the main reason is that the same noise level on a higher resolution results in a higher Signal-to-Noise Ratio in the frequency domain. In this work, we present Relay Diffusion Model (RDM), which transfers a low-resolution image or noise into an equivalent high-resolution one for diffusion model via blurring diffusion and block noise. Therefore, the diffusion process can continue seamlessly in any new resolution or model without restarting from pure noise or low-resolution conditioning. RDM achieves state-of-the-art FID on CelebA-HQ and sFID on ImageNet 256times256, surpassing previous works such as ADM, LDM and DiT by a large margin. All the codes and checkpoints are open-sourced at https://github.com/THUDM/RelayDiffusion.

Generative models have made significant impacts across various domains, largely due to their ability to scale during training by increasing data, computational resources, and model size, a phenomenon characterized by the scaling laws. Recent research has begun to explore inference-time scaling behavior in Large Language Models (LLMs), revealing how performance can further improve with additional computation during inference. Unlike LLMs, diffusion models inherently possess the flexibility to adjust inference-time computation via the number of denoising steps, although the performance gains typically flatten after a few dozen. In this work, we explore the inference-time scaling behavior of diffusion models beyond increasing denoising steps and investigate how the generation performance can further improve with increased computation. Specifically, we consider a search problem aimed at identifying better noises for the diffusion sampling process. We structure the design space along two axes: the verifiers used to provide feedback, and the algorithms used to find better noise candidates. Through extensive experiments on class-conditioned and text-conditioned image generation benchmarks, our findings reveal that increasing inference-time compute leads to substantial improvements in the quality of samples generated by diffusion models, and with the complicated nature of images, combinations of the components in the framework can be specifically chosen to conform with different application scenario.

In this study, we examine the representation learning abilities of Denoising Diffusion Models (DDM) that were originally purposed for image generation. Our philosophy is to deconstruct a DDM, gradually transforming it into a classical Denoising Autoencoder (DAE). This deconstructive procedure allows us to explore how various components of modern DDMs influence self-supervised representation learning. We observe that only a very few modern components are critical for learning good representations, while many others are nonessential. Our study ultimately arrives at an approach that is highly simplified and to a large extent resembles a classical DAE. We hope our study will rekindle interest in a family of classical methods within the realm of modern self-supervised learning.

Diffusion models have achieved remarkable success in image and video generation. In this work, we demonstrate that diffusion models can also generate high-performing neural network parameters. Our approach is simple, utilizing an autoencoder and a standard latent diffusion model. The autoencoder extracts latent representations of a subset of the trained network parameters. A diffusion model is then trained to synthesize these latent parameter representations from random noise. It then generates new representations that are passed through the autoencoder's decoder, whose outputs are ready to use as new subsets of network parameters. Across various architectures and datasets, our diffusion process consistently generates models of comparable or improved performance over trained networks, with minimal additional cost. Notably, we empirically find that the generated models perform differently with the trained networks. Our results encourage more exploration on the versatile use of diffusion models.

Diffusion models have become the go-to method for large-scale generative models in real-world applications. These applications often involve data distributions confined within bounded domains, typically requiring ad-hoc thresholding techniques for boundary enforcement. Reflected diffusion models (Lou23) aim to enhance generalizability by generating the data distribution through a backward process governed by reflected Brownian motion. However, reflected diffusion models may not easily adapt to diverse domains without the derivation of proper diffeomorphic mappings and do not guarantee optimal transport properties. To overcome these limitations, we introduce the Reflected Schrodinger Bridge algorithm: an entropy-regularized optimal transport approach tailored for generating data within diverse bounded domains. We derive elegant reflected forward-backward stochastic differential equations with Neumann and Robin boundary conditions, extend divergence-based likelihood training to bounded domains, and explore natural connections to entropic optimal transport for the study of approximate linear convergence - a valuable insight for practical training. Our algorithm yields robust generative modeling in diverse domains, and its scalability is demonstrated in real-world constrained generative modeling through standard image benchmarks.

Autoregressive (AR) Large Language Models (LLMs) have demonstrated significant success across numerous tasks. However, the AR modeling paradigm presents certain limitations; for instance, contemporary autoregressive LLMs are trained to generate one token at a time, which can result in noticeable latency. Recent advances have indicated that search and repeated sampling can enhance performance in various applications, such as theorem proving, code generation, and alignment, by utilizing greater computational resources during inference. In this study, we demonstrate that diffusion language models are capable of generating at least 32 tokens simultaneously, while exceeding the performance of AR models in text quality and on the LAMBADA natural language understanding benchmark. This outcome is achieved through a novel distillation method for discrete diffusion models, which reduces the number of inference steps by a factor of 32-64. Practically, our models, even without caching, can generate tokens at a rate that is up to 8 times faster than AR models employing KV caching, and we anticipate further improvements with the inclusion of caching. Moreover, we demonstrate the efficacy of our approach for diffusion language models with up to 860M parameters.

This paper presents a comprehensive study on the unified module for accelerating stable-diffusion processes, specifically focusing on the lcm-lora module. Stable-diffusion processes play a crucial role in various scientific and engineering domains, and their acceleration is of paramount importance for efficient computational performance. The standard iterative procedures for solving fixed-source discrete ordinates problems often exhibit slow convergence, particularly in optically thick scenarios. To address this challenge, unconditionally stable diffusion-acceleration methods have been developed, aiming to enhance the computational efficiency of transport equations and discrete ordinates problems. This study delves into the theoretical foundations and numerical results of unconditionally stable diffusion synthetic acceleration methods, providing insights into their stability and performance for model discrete ordinates problems. Furthermore, the paper explores recent advancements in diffusion model acceleration, including on device acceleration of large diffusion models via gpu aware optimizations, highlighting the potential for significantly improved inference latency. The results and analyses in this study provide important insights into stable diffusion processes and have important ramifications for the creation and application of acceleration methods specifically, the lcm-lora module in a variety of computing environments.

Diffusion models have shown incredible capabilities as generative models; indeed, they power the current state-of-the-art models on text-conditioned image generation such as Imagen and DALL-E 2. In this work we review, demystify, and unify the understanding of diffusion models across both variational and score-based perspectives. We first derive Variational Diffusion Models (VDM) as a special case of a Markovian Hierarchical Variational Autoencoder, where three key assumptions enable tractable computation and scalable optimization of the ELBO. We then prove that optimizing a VDM boils down to learning a neural network to predict one of three potential objectives: the original source input from any arbitrary noisification of it, the original source noise from any arbitrarily noisified input, or the score function of a noisified input at any arbitrary noise level. We then dive deeper into what it means to learn the score function, and connect the variational perspective of a diffusion model explicitly with the Score-based Generative Modeling perspective through Tweedie's Formula. Lastly, we cover how to learn a conditional distribution using diffusion models via guidance.

Diffusion models have shown tremendous results in image generation. However, due to the iterative nature of the diffusion process and its reliance on classifier-free guidance, inference times are slow. In this paper, we propose a new distillation approach for guided diffusion models in which an external lightweight guide model is trained while the original text-to-image model remains frozen. We show that our method reduces the inference computation of classifier-free guided latent-space diffusion models by almost half, and only requires 1\% trainable parameters of the base model. Furthermore, once trained, our guide model can be applied to various fine-tuned, domain-specific versions of the base diffusion model without the need for additional training: this "plug-and-play" functionality drastically improves inference computation while maintaining the visual fidelity of generated images. Empirically, we show that our approach is able to produce visually appealing results and achieve a comparable FID score to the teacher with as few as 8 to 16 steps.

Diffusion models, such as Stable Diffusion (SD), offer the ability to generate high-resolution images with diverse features, but they come at a significant computational and memory cost. In classifier-free guided diffusion models, prolonged inference times are attributed to the necessity of computing two separate diffusion models at each denoising step. Recent work has shown promise in improving inference time through distillation techniques, teaching the model to perform similar denoising steps with reduced computations. However, the application of distillation introduces additional memory overhead to these already resource-intensive diffusion models, making it less practical. To address these challenges, our research explores a novel approach that combines Low-Rank Adaptation (LoRA) with model distillation to efficiently compress diffusion models. This approach not only reduces inference time but also mitigates memory overhead, and notably decreases memory consumption even before applying distillation. The results are remarkable, featuring a significant reduction in inference time due to the distillation process and a substantial 50% reduction in memory consumption. Our examination of the generated images underscores that the incorporation of LoRA-enhanced distillation maintains image quality and alignment with the provided prompts. In summary, while conventional distillation tends to increase memory consumption, LoRA-enhanced distillation offers optimization without any trade-offs or compromises in quality.

Diffusion models are a class of flexible generative models trained with an approximation to the log-likelihood objective. However, most use cases of diffusion models are not concerned with likelihoods, but instead with downstream objectives such as human-perceived image quality or drug effectiveness. In this paper, we investigate reinforcement learning methods for directly optimizing diffusion models for such objectives. We describe how posing denoising as a multi-step decision-making problem enables a class of policy gradient algorithms, which we refer to as denoising diffusion policy optimization (DDPO), that are more effective than alternative reward-weighted likelihood approaches. Empirically, DDPO is able to adapt text-to-image diffusion models to objectives that are difficult to express via prompting, such as image compressibility, and those derived from human feedback, such as aesthetic quality. Finally, we show that DDPO can improve prompt-image alignment using feedback from a vision-language model without the need for additional data collection or human annotation.

Recent advances in Conditional Diffusion Models have led to substantial capabilities in various domains. However, understanding the impact of variations in the initial seed vector remains an underexplored area of concern. Particularly, latent-based diffusion models display inconsistencies in image generation under standard conditions when initialized with suboptimal initial seed vectors. To understand the impact of the initial seed vector on generated samples, we propose a reliability evaluation framework that evaluates the generated samples of a diffusion model when the initial seed vector is subjected to various synthetic shifts. Our results indicate that slight manipulations to the initial seed vector of the state-of-the-art Stable Diffusion (Rombach et al., 2022) can lead to significant disturbances in the generated samples, consequently creating images without the effect of conditioning variables. In contrast, GLIDE (Nichol et al., 2022) stands out in generating reliable samples even when the initial seed vector is transformed. Thus, our study sheds light on the importance of the selection and the impact of the initial seed vector in the latent-based diffusion model.

A diffusion model learns to predict a vector field of gradients. We propose to apply chain rule on the learned gradients, and back-propagate the score of a diffusion model through the Jacobian of a differentiable renderer, which we instantiate to be a voxel radiance field. This setup aggregates 2D scores at multiple camera viewpoints into a 3D score, and repurposes a pretrained 2D model for 3D data generation. We identify a technical challenge of distribution mismatch that arises in this application, and propose a novel estimation mechanism to resolve it. We run our algorithm on several off-the-shelf diffusion image generative models, including the recently released Stable Diffusion trained on the large-scale LAION dataset.

Diffusion model (DM) has achieved SOTA performance by modeling the image synthesis process into a sequential application of a denoising network. However, different from image synthesis, image restoration (IR) has a strong constraint to generate results in accordance with ground-truth. Thus, for IR, traditional DMs running massive iterations on a large model to estimate whole images or feature maps is inefficient. To address this issue, we propose an efficient DM for IR (DiffIR), which consists of a compact IR prior extraction network (CPEN), dynamic IR transformer (DIRformer), and denoising network. Specifically, DiffIR has two training stages: pretraining and training DM. In pretraining, we input ground-truth images into CPEN_{S1} to capture a compact IR prior representation (IPR) to guide DIRformer. In the second stage, we train the DM to directly estimate the same IRP as pretrained CPEN_{S1} only using LQ images. We observe that since the IPR is only a compact vector, DiffIR can use fewer iterations than traditional DM to obtain accurate estimations and generate more stable and realistic results. Since the iterations are few, our DiffIR can adopt a joint optimization of CPEN_{S2}, DIRformer, and denoising network, which can further reduce the estimation error influence. We conduct extensive experiments on several IR tasks and achieve SOTA performance while consuming less computational costs. Code is available at https://github.com/Zj-BinXia/DiffIR.

Preference optimization for diffusion models aims to align them with human preferences for images. Previous methods typically leverage Vision-Language Models (VLMs) as pixel-level reward models to approximate human preferences. However, when used for step-level preference optimization, these models face challenges in handling noisy images of different timesteps and require complex transformations into pixel space. In this work, we demonstrate that diffusion models are inherently well-suited for step-level reward modeling in the latent space, as they can naturally extract features from noisy latent images. Accordingly, we propose the Latent Reward Model (LRM), which repurposes components of diffusion models to predict preferences of latent images at various timesteps. Building on LRM, we introduce Latent Preference Optimization (LPO), a method designed for step-level preference optimization directly in the latent space. Experimental results indicate that LPO not only significantly enhances performance in aligning diffusion models with general, aesthetic, and text-image alignment preferences, but also achieves 2.5-28times training speedup compared to existing preference optimization methods. Our code will be available at https://github.com/casiatao/LPO.

Masked (or absorbing) diffusion is actively explored as an alternative to autoregressive models for generative modeling of discrete data. However, existing work in this area has been hindered by unnecessarily complex model formulations and unclear relationships between different perspectives, leading to suboptimal parameterization, training objectives, and ad hoc adjustments to counteract these issues. In this work, we aim to provide a simple and general framework that unlocks the full potential of masked diffusion models. We show that the continuous-time variational objective of masked diffusion models is a simple weighted integral of cross-entropy losses. Our framework also enables training generalized masked diffusion models with state-dependent masking schedules. When evaluated by perplexity, our models trained on OpenWebText surpass prior diffusion language models at GPT-2 scale and demonstrate superior performance on 4 out of 5 zero-shot language modeling tasks. Furthermore, our models vastly outperform previous discrete diffusion models on pixel-level image modeling, achieving 2.78~(CIFAR-10) and 3.42 (ImageNet 64times64) bits per dimension that are comparable or better than autoregressive models of similar sizes.

We present DiffusionBERT, a new generative masked language model based on discrete diffusion models. Diffusion models and many pre-trained language models have a shared training objective, i.e., denoising, making it possible to combine the two powerful models and enjoy the best of both worlds. On the one hand, diffusion models offer a promising training strategy that helps improve the generation quality. On the other hand, pre-trained denoising language models (e.g., BERT) can be used as a good initialization that accelerates convergence. We explore training BERT to learn the reverse process of a discrete diffusion process with an absorbing state and elucidate several designs to improve it. First, we propose a new noise schedule for the forward diffusion process that controls the degree of noise added at each step based on the information of each token. Second, we investigate several designs of incorporating the time step into BERT. Experiments on unconditional text generation demonstrate that DiffusionBERT achieves significant improvement over existing diffusion models for text (e.g., D3PM and Diffusion-LM) and previous generative masked language models in terms of perplexity and BLEU score.

Diffusion models have emerged as the new state-of-the-art generative model with high quality samples, with intriguing properties such as mode coverage and high flexibility. They have also been shown to be effective inverse problem solvers, acting as the prior of the distribution, while the information of the forward model can be granted at the sampling stage. Nonetheless, as the generative process remains in the same high dimensional (i.e. identical to data dimension) space, the models have not been extended to 3D inverse problems due to the extremely high memory and computational cost. In this paper, we combine the ideas from the conventional model-based iterative reconstruction with the modern diffusion models, which leads to a highly effective method for solving 3D medical image reconstruction tasks such as sparse-view tomography, limited angle tomography, compressed sensing MRI from pre-trained 2D diffusion models. In essence, we propose to augment the 2D diffusion prior with a model-based prior in the remaining direction at test time, such that one can achieve coherent reconstructions across all dimensions. Our method can be run in a single commodity GPU, and establishes the new state-of-the-art, showing that the proposed method can perform reconstructions of high fidelity and accuracy even in the most extreme cases (e.g. 2-view 3D tomography). We further reveal that the generalization capacity of the proposed method is surprisingly high, and can be used to reconstruct volumes that are entirely different from the training dataset.

Although diffusion models (DMs) have shown promising performances in a number of tasks (e.g., speech synthesis and image generation), they might suffer from error propagation because of their sequential structure. However, this is not certain because some sequential models, such as Conditional Random Field (CRF), are free from this problem. To address this issue, we develop a theoretical framework to mathematically formulate error propagation in the architecture of DMs, The framework contains three elements, including modular error, cumulative error, and propagation equation. The modular and cumulative errors are related by the equation, which interprets that DMs are indeed affected by error propagation. Our theoretical study also suggests that the cumulative error is closely related to the generation quality of DMs. Based on this finding, we apply the cumulative error as a regularization term to reduce error propagation. Because the term is computationally intractable, we derive its upper bound and design a bootstrap algorithm to efficiently estimate the bound for optimization. We have conducted extensive experiments on multiple image datasets, showing that our proposed regularization reduces error propagation, significantly improves vanilla DMs, and outperforms previous baselines.

Denoising diffusion probabilistic models have transformed image generation with their impressive fidelity and diversity. We show that they also excel in estimating optical flow and monocular depth, surprisingly, without task-specific architectures and loss functions that are predominant for these tasks. Compared to the point estimates of conventional regression-based methods, diffusion models also enable Monte Carlo inference, e.g., capturing uncertainty and ambiguity in flow and depth. With self-supervised pre-training, the combined use of synthetic and real data for supervised training, and technical innovations (infilling and step-unrolled denoising diffusion training) to handle noisy-incomplete training data, and a simple form of coarse-to-fine refinement, one can train state-of-the-art diffusion models for depth and optical flow estimation. Extensive experiments focus on quantitative performance against benchmarks, ablations, and the model's ability to capture uncertainty and multimodality, and impute missing values. Our model, DDVM (Denoising Diffusion Vision Model), obtains a state-of-the-art relative depth error of 0.074 on the indoor NYU benchmark and an Fl-all outlier rate of 3.26\% on the KITTI optical flow benchmark, about 25\% better than the best published method. For an overview see https://diffusion-vision.github.io.

Limited-Angle Computed Tomography (LACT) is a non-destructive evaluation technique used in a variety of applications ranging from security to medicine. The limited angle coverage in LACT is often a dominant source of severe artifacts in the reconstructed images, making it a challenging inverse problem. We present DOLCE, a new deep model-based framework for LACT that uses a conditional diffusion model as an image prior. Diffusion models are a recent class of deep generative models that are relatively easy to train due to their implementation as image denoisers. DOLCE can form high-quality images from severely under-sampled data by integrating data-consistency updates with the sampling updates of a diffusion model, which is conditioned on the transformed limited-angle data. We show through extensive experimentation on several challenging real LACT datasets that, the same pre-trained DOLCE model achieves the SOTA performance on drastically different types of images. Additionally, we show that, unlike standard LACT reconstruction methods, DOLCE naturally enables the quantification of the reconstruction uncertainty by generating multiple samples consistent with the measured data.

Despite the growing success of diffusion models in continuous-valued domains (e.g., images), similar efforts for discrete domains such as text have yet to match the performance of autoregressive language models. In this work, we present SSD-LM -- a diffusion-based language model with two key design choices. First, SSD-LM is semi-autoregressive, iteratively generating blocks of text, allowing for flexible output length at decoding time while enabling local bidirectional context updates. Second, it is simplex-based, performing diffusion on the natural vocabulary space rather than a learned latent space, allowing us to incorporate classifier guidance and modular control using off-the-shelf classifiers without any adaptation. We evaluate SSD-LM on unconstrained text generation benchmarks, and show that it matches or outperforms strong autoregressive GPT-2 models across standard quality and diversity metrics, while vastly outperforming diffusion-based baselines. On controlled text generation, SSD-LM also outperforms competitive baselines, with an extra advantage in modularity.

Diffusion models have established themselves as state-of-the-art generative models across various data modalities, including images and videos, due to their ability to accurately approximate complex data distributions. Unlike traditional generative approaches such as VAEs and GANs, diffusion models employ a progressive denoising process that transforms noise into meaningful data over multiple iterative steps. This gradual approach enhances their expressiveness and generation quality. Not only that, diffusion models have also been shown to extract meaningful representations from data while learning to generate samples. Despite their success, the application of diffusion models to graph-structured data remains relatively unexplored, primarily due to the discrete nature of graphs, which necessitates discrete diffusion processes distinct from the continuous methods used in other domains. In this work, we leverage the representational capabilities of diffusion models to learn meaningful embeddings for graph data. By training a discrete diffusion model within an autoencoder framework, we enable both effective autoencoding and representation learning tailored to the unique characteristics of graph-structured data. We only need the encoder at the end to extract representations. Our approach demonstrates the potential of discrete diffusion models to be used for graph representation learning.

Diffusion models achieve state-of-the-art performance in various generation tasks. However, their theoretical foundations fall far behind. This paper studies score approximation, estimation, and distribution recovery of diffusion models, when data are supported on an unknown low-dimensional linear subspace. Our result provides sample complexity bounds for distribution estimation using diffusion models. We show that with a properly chosen neural network architecture, the score function can be both accurately approximated and efficiently estimated. Furthermore, the generated distribution based on the estimated score function captures the data geometric structures and converges to a close vicinity of the data distribution. The convergence rate depends on the subspace dimension, indicating that diffusion models can circumvent the curse of data ambient dimensionality.

We present the first framework to solve linear inverse problems leveraging pre-trained latent diffusion models. Previously proposed algorithms (such as DPS and DDRM) only apply to pixel-space diffusion models. We theoretically analyze our algorithm showing provable sample recovery in a linear model setting. The algorithmic insight obtained from our analysis extends to more general settings often considered in practice. Experimentally, we outperform previously proposed posterior sampling algorithms in a wide variety of problems including random inpainting, block inpainting, denoising, deblurring, destriping, and super-resolution.

Diffusion (score-based) generative models have been widely used for modeling various types of complex data, including images, audios, and point clouds. Recently, the deep connection between forward-backward stochastic differential equations (SDEs) and diffusion-based models has been revealed, and several new variants of SDEs are proposed (e.g., sub-VP, critically-damped Langevin) along this line. Despite the empirical success of the hand-crafted fixed forward SDEs, a great quantity of proper forward SDEs remain unexplored. In this work, we propose a general framework for parameterizing the diffusion model, especially the spatial part of the forward SDE. An abstract formalism is introduced with theoretical guarantees, and its connection with previous diffusion models is leveraged. We demonstrate the theoretical advantage of our method from an optimization perspective. Numerical experiments on synthetic datasets, MINIST and CIFAR10 are also presented to validate the effectiveness of our framework.

In recent years, denoising diffusion models have become a crucial area of research due to their abundance in the rapidly expanding field of generative AI. While recent statistical advances have delivered explanations for the generation ability of idealised denoising diffusion models for high-dimensional target data, implementations introduce thresholding procedures for the generating process to overcome issues arising from the unbounded state space of such models. This mismatch between theoretical design and implementation of diffusion models has been addressed empirically by using a reflected diffusion process as the driver of noise instead. In this paper, we study statistical guarantees of these denoising reflected diffusion models. In particular, we establish minimax optimal rates of convergence in total variation, up to a polylogarithmic factor, under Sobolev smoothness assumptions. Our main contributions include the statistical analysis of this novel class of denoising reflected diffusion models and a refined score approximation method in both time and space, leveraging spectral decomposition and rigorous neural network analysis.

Applying diffusion models in reinforcement learning for long-term planning has gained much attention recently. Several diffusion-based methods have successfully leveraged the modeling capabilities of diffusion for arbitrary distributions. These methods generate subsequent trajectories for planning and have demonstrated significant improvement. However, these methods are limited by their plain base distributions and their overlooking of the diversity of samples, in which different states have different returns. They simply leverage diffusion to learn the distribution of offline dataset, generate the trajectories whose states share the same distribution with the offline dataset. As a result, the probability of these models reaching the high-return states is largely dependent on the dataset distribution. Even equipped with the guidance model, the performance is still suppressed. To address these limitations, in this paper, we propose a novel method called CDiffuser, which devises a return contrast mechanism to pull the states in generated trajectories towards high-return states while pushing them away from low-return states to improve the base distribution. Experiments on 14 commonly used D4RL benchmarks demonstrate the effectiveness of our proposed method.

Diffusion models have emerged as a pivotal advancement in generative models, setting new standards to the quality of the generated instances. In the current paper we aim to underscore a discrepancy between conventional training methods and the desired conditional sampling behavior of these models. While the prevalent classifier-free guidance technique works well, it's not without flaws. At higher values for the guidance scale parameter w, we often get out of distribution samples and mode collapse, whereas at lower values for w we may not get the desired specificity. To address these challenges, we introduce an updated loss function that better aligns training objectives with sampling behaviors. Experimental validation with FID scores on CIFAR-10 elucidates our method's ability to produce higher quality samples with fewer sampling timesteps, and be more robust to the choice of guidance scale w. We also experiment with fine-tuning Stable Diffusion on the proposed loss, to provide early evidence that large diffusion models may also benefit from this refined loss function.

Recent advancements in latent diffusion models (LDMs) have markedly enhanced text-to-audio generation, yet their iterative sampling processes impose substantial computational demands, limiting practical deployment. While recent methods utilizing consistency-based distillation aim to achieve few-step or single-step inference, their one-step performance is constrained by curved trajectories, preventing them from surpassing traditional diffusion models. In this work, we introduce FlashAudio with rectified flows to learn straight flow for fast simulation. To alleviate the inefficient timesteps allocation and suboptimal distribution of noise, FlashAudio optimizes the time distribution of rectified flow with Bifocal Samplers and proposes immiscible flow to minimize the total distance of data-noise pairs in a batch vias assignment. Furthermore, to address the amplified accumulation error caused by the classifier-free guidance (CFG), we propose Anchored Optimization, which refines the guidance scale by anchoring it to a reference trajectory. Experimental results on text-to-audio generation demonstrate that FlashAudio's one-step generation performance surpasses the diffusion-based models with hundreds of sampling steps on audio quality and enables a sampling speed of 400x faster than real-time on a single NVIDIA 4090Ti GPU.

While diffusion models can successfully generate data and make predictions, they are predominantly designed for static images. We propose an approach for efficiently training diffusion models for probabilistic spatiotemporal forecasting, where generating stable and accurate rollout forecasts remains challenging, Our method, DYffusion, leverages the temporal dynamics in the data, directly coupling it with the diffusion steps in the model. We train a stochastic, time-conditioned interpolator and a forecaster network that mimic the forward and reverse processes of standard diffusion models, respectively. DYffusion naturally facilitates multi-step and long-range forecasting, allowing for highly flexible, continuous-time sampling trajectories and the ability to trade-off performance with accelerated sampling at inference time. In addition, the dynamics-informed diffusion process in DYffusion imposes a strong inductive bias and significantly improves computational efficiency compared to traditional Gaussian noise-based diffusion models. Our approach performs competitively on probabilistic forecasting of complex dynamics in sea surface temperatures, Navier-Stokes flows, and spring mesh systems.

Despite remarkable progress in autoregressive language models, alternative generative paradigms beyond left-to-right generation are still being actively explored. Discrete diffusion models, with the capacity for parallel generation, have recently emerged as a promising alternative. Unfortunately, these models still underperform the autoregressive counterparts, with the performance gap increasing when reducing the number of sampling steps. Our analysis reveals that this degradation is a consequence of an imperfect approximation used by diffusion models. In this work, we propose Energy-based Diffusion Language Model (EDLM), an energy-based model operating at the full sequence level for each diffusion step, introduced to improve the underlying approximation used by diffusion models. More specifically, we introduce an EBM in a residual form, and show that its parameters can be obtained by leveraging a pretrained autoregressive model or by finetuning a bidirectional transformer via noise contrastive estimation. We also propose an efficient generation algorithm via parallel important sampling. Comprehensive experiments on language modeling benchmarks show that our model can consistently outperform state-of-the-art diffusion models by a significant margin, and approaches autoregressive models' perplexity. We further show that, without any generation performance drop, our framework offers a 1.3times sampling speedup over existing diffusion models.

Diffusion-based generative models (DBGMs) perturb data to a target noise distribution and reverse this process to generate samples. The choice of noising process, or inference diffusion process, affects both likelihoods and sample quality. For example, extending the inference process with auxiliary variables leads to improved sample quality. While there are many such multivariate diffusions to explore, each new one requires significant model-specific analysis, hindering rapid prototyping and evaluation. In this work, we study Multivariate Diffusion Models (MDMs). For any number of auxiliary variables, we provide a recipe for maximizing a lower-bound on the MDMs likelihood without requiring any model-specific analysis. We then demonstrate how to parameterize the diffusion for a specified target noise distribution; these two points together enable optimizing the inference diffusion process. Optimizing the diffusion expands easy experimentation from just a few well-known processes to an automatic search over all linear diffusions. To demonstrate these ideas, we introduce two new specific diffusions as well as learn a diffusion process on the MNIST, CIFAR10, and ImageNet32 datasets. We show learned MDMs match or surpass bits-per-dims (BPDs) relative to fixed choices of diffusions for a given dataset and model architecture.

Magnetic resonance imaging (MRI) is a common and life-saving medical imaging technique. However, acquiring high signal-to-noise ratio MRI scans requires long scan times, resulting in increased costs and patient discomfort, and decreased throughput. Thus, there is great interest in denoising MRI scans, especially for the subtype of diffusion MRI scans that are severely SNR-limited. While most prior MRI denoising methods are supervised in nature, acquiring supervised training datasets for the multitude of anatomies, MRI scanners, and scan parameters proves impractical. Here, we propose Denoising Diffusion Models for Denoising Diffusion MRI (DDM^2), a self-supervised denoising method for MRI denoising using diffusion denoising generative models. Our three-stage framework integrates statistic-based denoising theory into diffusion models and performs denoising through conditional generation. During inference, we represent input noisy measurements as a sample from an intermediate posterior distribution within the diffusion Markov chain. We conduct experiments on 4 real-world in-vivo diffusion MRI datasets and show that our DDM^2 demonstrates superior denoising performances ascertained with clinically-relevant visual qualitative and quantitative metrics.

Denoising Diffusion Probabilistic Models (DDPMs) achieve state-of-the-art performance in synthesizing new images from random noise, but they lack meaningful latent space that encodes data into features. Recent DDPM-based editing techniques try to mitigate this issue by inverting images back to their approximated staring noise. In this work, we study the relation between the initial Gaussian noise, the samples generated from it, and their corresponding latent encodings obtained through the inversion procedure. First, we interpret their spatial distance relations to show the inaccuracy of the DDIM inversion technique by localizing latent representations manifold between the initial noise and generated samples. Then, we demonstrate the peculiar relation between initial Gaussian noise and its corresponding generations during diffusion training, showing that the high-level features of generated images stabilize rapidly, keeping the spatial distance relationship between noises and generations consistent throughout the training.

In recent advancements in high-fidelity image generation, Denoising Diffusion Probabilistic Models (DDPMs) have emerged as a key player. However, their application at high resolutions presents significant computational challenges. Current methods, such as patchifying, expedite processes in UNet and Transformer architectures but at the expense of representational capacity. Addressing this, we introduce the Diffusion State Space Model (DiffuSSM), an architecture that supplants attention mechanisms with a more scalable state space model backbone. This approach effectively handles higher resolutions without resorting to global compression, thus preserving detailed image representation throughout the diffusion process. Our focus on FLOP-efficient architectures in diffusion training marks a significant step forward. Comprehensive evaluations on both ImageNet and LSUN datasets at two resolutions demonstrate that DiffuSSMs are on par or even outperform existing diffusion models with attention modules in FID and Inception Score metrics while significantly reducing total FLOP usage.

Denoising diffusion models (DDMs) have recently attracted increasing attention by showing impressive synthesis quality. DDMs are built on a diffusion process that pushes data to the noise distribution and the models learn to denoise. In this paper, we establish the interpretation of DDMs in terms of image restoration (IR). Integrating IR literature allows us to use an alternative objective and diverse forward processes, not confining to the diffusion process. By imposing prior knowledge on the loss function grounded on MAP-based estimation, we eliminate the need for the expensive sampling of DDMs. Also, we propose a multi-scale training, which improves the performance compared to the diffusion process, by taking advantage of the flexibility of the forward process. Experimental results demonstrate that our model improves the quality and efficiency of both training and inference. Furthermore, we show the applicability of our model to inverse problems. We believe that our framework paves the way for designing a new type of flexible general generative model.

Learning diffusion bridge models is easy; making them fast and practical is an art. Diffusion bridge models (DBMs) are a promising extension of diffusion models for applications in image-to-image translation. However, like many modern diffusion and flow models, DBMs suffer from the problem of slow inference. To address it, we propose a novel distillation technique based on the inverse bridge matching formulation and derive the tractable objective to solve it in practice. Unlike previously developed DBM distillation techniques, the proposed method can distill both conditional and unconditional types of DBMs, distill models in a one-step generator, and use only the corrupted images for training. We evaluate our approach for both conditional and unconditional types of bridge matching on a wide set of setups, including super-resolution, JPEG restoration, sketch-to-image, and other tasks, and show that our distillation technique allows us to accelerate the inference of DBMs from 4x to 100x and even provide better generation quality than used teacher model depending on particular setup.

Denoising is intuitively related to projection. Indeed, under the manifold hypothesis, adding random noise is approximately equivalent to orthogonal perturbation. Hence, learning to denoise is approximately learning to project. In this paper, we use this observation to reinterpret denoising diffusion models as approximate gradient descent applied to the Euclidean distance function. We then provide straight-forward convergence analysis of the DDIM sampler under simple assumptions on the projection-error of the denoiser. Finally, we propose a new sampler based on two simple modifications to DDIM using insights from our theoretical results. In as few as 5-10 function evaluations, our sampler achieves state-of-the-art FID scores on pretrained CIFAR-10 and CelebA models and can generate high quality samples on latent diffusion models.

Denoising diffusion (score-based) generative models have recently achieved significant accomplishments in generating realistic and diverse data. These approaches define a forward diffusion process for transforming data into noise and a backward denoising process for sampling data from noise. Unfortunately, the generation process of current denoising diffusion models is notoriously slow due to the lengthy iterative noise estimations, which rely on cumbersome neural networks. It prevents the diffusion models from being widely deployed, especially on edge devices. Previous works accelerate the generation process of diffusion model (DM) via finding shorter yet effective sampling trajectories. However, they overlook the cost of noise estimation with a heavy network in every iteration. In this work, we accelerate generation from the perspective of compressing the noise estimation network. Due to the difficulty of retraining DMs, we exclude mainstream training-aware compression paradigms and introduce post-training quantization (PTQ) into DM acceleration. However, the output distributions of noise estimation networks change with time-step, making previous PTQ methods fail in DMs since they are designed for single-time step scenarios. To devise a DM-specific PTQ method, we explore PTQ on DM in three aspects: quantized operations, calibration dataset, and calibration metric. We summarize and use several observations derived from all-inclusive investigations to formulate our method, which especially targets the unique multi-time-step structure of DMs. Experimentally, our method can directly quantize full-precision DMs into 8-bit models while maintaining or even improving their performance in a training-free manner. Importantly, our method can serve as a plug-and-play module on other fast-sampling methods, e.g., DDIM. The code is available at https://github.com/42Shawn/PTQ4DM .

The past few years have witnessed the great success of Diffusion models~(DMs) in generating high-fidelity samples in generative modeling tasks. A major limitation of the DM is its notoriously slow sampling procedure which normally requires hundreds to thousands of time discretization steps of the learned diffusion process to reach the desired accuracy. Our goal is to develop a fast sampling method for DMs with a much less number of steps while retaining high sample quality. To this end, we systematically analyze the sampling procedure in DMs and identify key factors that affect the sample quality, among which the method of discretization is most crucial. By carefully examining the learned diffusion process, we propose Diffusion Exponential Integrator Sampler~(DEIS). It is based on the Exponential Integrator designed for discretizing ordinary differential equations (ODEs) and leverages a semilinear structure of the learned diffusion process to reduce the discretization error. The proposed method can be applied to any DMs and can generate high-fidelity samples in as few as 10 steps. In our experiments, it takes about 3 minutes on one A6000 GPU to generate 50k images from CIFAR10. Moreover, by directly using pre-trained DMs, we achieve the state-of-art sampling performance when the number of score function evaluation~(NFE) is limited, e.g., 4.17 FID with 10 NFEs, 3.37 FID, and 9.74 IS with only 15 NFEs on CIFAR10. Code is available at https://github.com/qsh-zh/deis

Conventional diffusion models typically relies on a fixed forward process, which implicitly defines complex marginal distributions over latent variables. This can often complicate the reverse process' task in learning generative trajectories, and results in costly inference for diffusion models. To address these limitations, we introduce Neural Flow Diffusion Models (NFDM), a novel framework that enhances diffusion models by supporting a broader range of forward processes beyond the fixed linear Gaussian. We also propose a novel parameterization technique for learning the forward process. Our framework provides an end-to-end, simulation-free optimization objective, effectively minimizing a variational upper bound on the negative log-likelihood. Experimental results demonstrate NFDM's strong performance, evidenced by state-of-the-art likelihood estimation. Furthermore, we investigate NFDM's capacity for learning generative dynamics with specific characteristics, such as deterministic straight lines trajectories. This exploration underscores NFDM's versatility and its potential for a wide range of applications.

Diffusion probabilistic models (DPMs) are emerging powerful generative models. Despite their high-quality generation performance, DPMs still suffer from their slow sampling as they generally need hundreds or thousands of sequential function evaluations (steps) of large neural networks to draw a sample. Sampling from DPMs can be viewed alternatively as solving the corresponding diffusion ordinary differential equations (ODEs). In this work, we propose an exact formulation of the solution of diffusion ODEs. The formulation analytically computes the linear part of the solution, rather than leaving all terms to black-box ODE solvers as adopted in previous works. By applying change-of-variable, the solution can be equivalently simplified to an exponentially weighted integral of the neural network. Based on our formulation, we propose DPM-Solver, a fast dedicated high-order solver for diffusion ODEs with the convergence order guarantee. DPM-Solver is suitable for both discrete-time and continuous-time DPMs without any further training. Experimental results show that DPM-Solver can generate high-quality samples in only 10 to 20 function evaluations on various datasets. We achieve 4.70 FID in 10 function evaluations and 2.87 FID in 20 function evaluations on the CIFAR10 dataset, and a 4sim 16times speedup compared with previous state-of-the-art training-free samplers on various datasets.

Diffusion models have demonstrated excellent potential for generating diverse images. However, their performance often suffers from slow generation due to iterative denoising. Knowledge distillation has been recently proposed as a remedy that can reduce the number of inference steps to one or a few without significant quality degradation. However, existing distillation methods either require significant amounts of offline computation for generating synthetic training data from the teacher model or need to perform expensive online learning with the help of real data. In this work, we present a novel technique called BOOT, that overcomes these limitations with an efficient data-free distillation algorithm. The core idea is to learn a time-conditioned model that predicts the output of a pre-trained diffusion model teacher given any time step. Such a model can be efficiently trained based on bootstrapping from two consecutive sampled steps. Furthermore, our method can be easily adapted to large-scale text-to-image diffusion models, which are challenging for conventional methods given the fact that the training sets are often large and difficult to access. We demonstrate the effectiveness of our approach on several benchmark datasets in the DDIM setting, achieving comparable generation quality while being orders of magnitude faster than the diffusion teacher. The text-to-image results show that the proposed approach is able to handle highly complex distributions, shedding light on more efficient generative modeling.

Latent variable generative models have emerged as powerful tools for generative tasks including image and video synthesis. These models are enabled by pretrained autoencoders that map high resolution data into a compressed lower dimensional latent space, where the generative models can subsequently be developed while requiring fewer computational resources. Despite their effectiveness, the direct application of latent variable models to higher dimensional domains such as videos continues to pose challenges for efficient training and inference. In this paper, we propose an autoencoder that projects volumetric data onto a four-plane factorized latent space that grows sublinearly with the input size, making it ideal for higher dimensional data like videos. The design of our factorized model supports straightforward adoption in a number of conditional generation tasks with latent diffusion models (LDMs), such as class-conditional generation, frame prediction, and video interpolation. Our results show that the proposed four-plane latent space retains a rich representation needed for high-fidelity reconstructions despite the heavy compression, while simultaneously enabling LDMs to operate with significant improvements in speed and memory.

Diffusion models (DMs) have shown remarkable capabilities in generating realistic high-quality images, audios, and videos. They benefit significantly from extensive pre-training on large-scale datasets, including web-crawled data with paired data and conditions, such as image-text and image-class pairs. Despite rigorous filtering, these pre-training datasets often inevitably contain corrupted pairs where conditions do not accurately describe the data. This paper presents the first comprehensive study on the impact of such corruption in pre-training data of DMs. We synthetically corrupt ImageNet-1K and CC3M to pre-train and evaluate over 50 conditional DMs. Our empirical findings reveal that various types of slight corruption in pre-training can significantly enhance the quality, diversity, and fidelity of the generated images across different DMs, both during pre-training and downstream adaptation stages. Theoretically, we consider a Gaussian mixture model and prove that slight corruption in the condition leads to higher entropy and a reduced 2-Wasserstein distance to the ground truth of the data distribution generated by the corruptly trained DMs. Inspired by our analysis, we propose a simple method to improve the training of DMs on practical datasets by adding condition embedding perturbations (CEP). CEP significantly improves the performance of various DMs in both pre-training and downstream tasks. We hope that our study provides new insights into understanding the data and pre-training processes of DMs.

Large language models (LLMs) based on decoder-only transformers have demonstrated superior text understanding capabilities compared to CLIP and T5-series models. However, the paradigm for utilizing current advanced LLMs in text-to-image diffusion models remains to be explored. We observed an unusual phenomenon: directly using a large language model as the prompt encoder significantly degrades the prompt-following ability in image generation. We identified two main obstacles behind this issue. One is the misalignment between the next token prediction training in LLM and the requirement for discriminative prompt features in diffusion models. The other is the intrinsic positional bias introduced by the decoder-only architecture. To deal with this issue, we propose a novel framework to fully harness the capabilities of LLMs. Through the carefully designed usage guidance, we effectively enhance the text representation capability for prompt encoding and eliminate its inherent positional bias. This allows us to integrate state-of-the-art LLMs into the text-to-image generation model flexibly. Furthermore, we also provide an effective manner to fuse multiple LLMs into our framework. Considering the excellent performance and scaling capabilities demonstrated by the transformer architecture, we further design an LLM-Infused Diffusion Transformer (LI-DiT) based on the framework. We conduct extensive experiments to validate LI-DiT across model size and data size. Benefiting from the inherent ability of the LLMs and our innovative designs, the prompt understanding performance of LI-DiT easily surpasses state-of-the-art open-source models as well as mainstream closed-source commercial models including Stable Diffusion 3, DALL-E 3, and Midjourney V6. The powerful LI-DiT-10B will be available after further optimization and security checks.

Score-based generative models (SGMs) are a powerful class of generative models that exhibit remarkable empirical performance. Score-based generative modelling (SGM) consists of a ``noising'' stage, whereby a diffusion is used to gradually add Gaussian noise to data, and a generative model, which entails a ``denoising'' process defined by approximating the time-reversal of the diffusion. Existing SGMs assume that data is supported on a Euclidean space, i.e. a manifold with flat geometry. In many domains such as robotics, geoscience or protein modelling, data is often naturally described by distributions living on Riemannian manifolds and current SGM techniques are not appropriate. We introduce here Riemannian Score-based Generative Models (RSGMs), a class of generative models extending SGMs to Riemannian manifolds. We demonstrate our approach on a variety of manifolds, and in particular with earth and climate science spherical data.

This paper describes an efficient algorithm for solving noisy linear inverse problems using pretrained diffusion models. Extending the paradigm of denoising diffusion implicit models (DDIM), we propose constrained diffusion implicit models (CDIM) that modify the diffusion updates to enforce a constraint upon the final output. For noiseless inverse problems, CDIM exactly satisfies the constraints; in the noisy case, we generalize CDIM to satisfy an exact constraint on the residual distribution of the noise. Experiments across a variety of tasks and metrics show strong performance of CDIM, with analogous inference acceleration to unconstrained DDIM: 10 to 50 times faster than previous conditional diffusion methods. We demonstrate the versatility of our approach on many problems including super-resolution, denoising, inpainting, deblurring, and 3D point cloud reconstruction.

Because diffusion models have shown impressive performances in a number of tasks, such as image synthesis, there is a trend in recent works to prove (with certain assumptions) that these models have strong approximation capabilities. In this paper, we show that current diffusion models actually have an expressive bottleneck in backward denoising and some assumption made by existing theoretical guarantees is too strong. Based on this finding, we prove that diffusion models have unbounded errors in both local and global denoising. In light of our theoretical studies, we introduce soft mixture denoising (SMD), an expressive and efficient model for backward denoising. SMD not only permits diffusion models to well approximate any Gaussian mixture distributions in theory, but also is simple and efficient for implementation. Our experiments on multiple image datasets show that SMD significantly improves different types of diffusion models (e.g., DDPM), espeically in the situation of few backward iterations.

Diffusion models have demonstrated compelling generation quality by optimizing the variational lower bound through a simple denoising score matching loss. In this paper, we provide theoretical evidence that the prevailing practice of using a constant loss weight strategy in diffusion models leads to biased estimation during the training phase. Simply optimizing the denoising network to predict Gaussian noise with constant weighting may hinder precise estimations of original images. To address the issue, we propose an elegant and effective weighting strategy grounded in the theoretically unbiased principle. Moreover, we conduct a comprehensive and systematic exploration to dissect the inherent bias problem deriving from constant weighting loss from the perspectives of its existence, impact and reasons. These analyses are expected to advance our understanding and demystify the inner workings of diffusion models. Through empirical evaluation, we demonstrate that our proposed debiased estimation method significantly enhances sample quality without the reliance on complex techniques, and exhibits improved efficiency compared to the baseline method both in training and sampling processes.

We introduce a Cascaded Diffusion Model (Cas-DM) that improves a Denoising Diffusion Probabilistic Model (DDPM) by effectively incorporating additional metric functions in training. Metric functions such as the LPIPS loss have been proven highly effective in consistency models derived from the score matching. However, for the diffusion counterparts, the methodology and efficacy of adding extra metric functions remain unclear. One major challenge is the mismatch between the noise predicted by a DDPM at each step and the desired clean image that the metric function works well on. To address this problem, we propose Cas-DM, a network architecture that cascades two network modules to effectively apply metric functions to the diffusion model training. The first module, similar to a standard DDPM, learns to predict the added noise and is unaffected by the metric function. The second cascaded module learns to predict the clean image, thereby facilitating the metric function computation. Experiment results show that the proposed diffusion model backbone enables the effective use of the LPIPS loss, leading to state-of-the-art image quality (FID, sFID, IS) on various established benchmarks.

While 2D diffusion models generate realistic, high-detail images, 3D shape generation methods like Score Distillation Sampling (SDS) built on these 2D diffusion models produce cartoon-like, over-smoothed shapes. To help explain this discrepancy, we show that the image guidance used in Score Distillation can be understood as the velocity field of a 2D denoising generative process, up to the choice of a noise term. In particular, after a change of variables, SDS resembles a high-variance version of Denoising Diffusion Implicit Models (DDIM) with a differently-sampled noise term: SDS introduces noise i.i.d. randomly at each step, while DDIM infers it from the previous noise predictions. This excessive variance can lead to over-smoothing and unrealistic outputs. We show that a better noise approximation can be recovered by inverting DDIM in each SDS update step. This modification makes SDS's generative process for 2D images almost identical to DDIM. In 3D, it removes over-smoothing, preserves higher-frequency detail, and brings the generation quality closer to that of 2D samplers. Experimentally, our method achieves better or similar 3D generation quality compared to other state-of-the-art Score Distillation methods, all without training additional neural networks or multi-view supervision, and providing useful insights into relationship between 2D and 3D asset generation with diffusion models.

Designing biological sequences is an important challenge that requires satisfying complex constraints and thus is a natural problem to address with deep generative modeling. Diffusion generative models have achieved considerable success in many applications. Score-based generative stochastic differential equations (SDE) model is a continuous-time diffusion model framework that enjoys many benefits, but the originally proposed SDEs are not naturally designed for modeling discrete data. To develop generative SDE models for discrete data such as biological sequences, here we introduce a diffusion process defined in the probability simplex space with stationary distribution being the Dirichlet distribution. This makes diffusion in continuous space natural for modeling discrete data. We refer to this approach as Dirchlet diffusion score model. We demonstrate that this technique can generate samples that satisfy hard constraints using a Sudoku generation task. This generative model can also solve Sudoku, including hard puzzles, without additional training. Finally, we applied this approach to develop the first human promoter DNA sequence design model and showed that designed sequences share similar properties with natural promoter sequences.

A popular approach to sample a diffusion-based generative model is to solve an ordinary differential equation (ODE). In existing samplers, the coefficients of the ODE solvers are pre-determined by the ODE formulation, the reverse discrete timesteps, and the employed ODE methods. In this paper, we consider accelerating several popular ODE-based sampling processes (including EDM, DDIM, and DPM-Solver) by optimizing certain coefficients via improved integration approximation (IIA). We propose to minimize, for each time step, a mean squared error (MSE) function with respect to the selected coefficients. The MSE is constructed by applying the original ODE solver for a set of fine-grained timesteps, which in principle provides a more accurate integration approximation in predicting the next diffusion state. The proposed IIA technique does not require any change of a pre-trained model, and only introduces a very small computational overhead for solving a number of quadratic optimization problems. Extensive experiments show that considerably better FID scores can be achieved by using IIA-EDM, IIA-DDIM, and IIA-DPM-Solver than the original counterparts when the neural function evaluation (NFE) is small (i.e., less than 25).

Diffusion-based generative models have shown great potential for image synthesis, but there is a lack of research on the security and privacy risks they may pose. In this paper, we investigate the vulnerability of diffusion models to Membership Inference Attacks (MIAs), a common privacy concern. Our results indicate that existing MIAs designed for GANs or VAE are largely ineffective on diffusion models, either due to inapplicable scenarios (e.g., requiring the discriminator of GANs) or inappropriate assumptions (e.g., closer distances between synthetic samples and member samples). To address this gap, we propose Step-wise Error Comparing Membership Inference (SecMI), a query-based MIA that infers memberships by assessing the matching of forward process posterior estimation at each timestep. SecMI follows the common overfitting assumption in MIA where member samples normally have smaller estimation errors, compared with hold-out samples. We consider both the standard diffusion models, e.g., DDPM, and the text-to-image diffusion models, e.g., Latent Diffusion Models and Stable Diffusion. Experimental results demonstrate that our methods precisely infer the membership with high confidence on both of the two scenarios across multiple different datasets. Code is available at https://github.com/jinhaoduan/SecMI.

While diffusion models excel at generating high-quality images, prior work reports a significant performance gap between diffusion and autoregressive (AR) methods in language modeling. In this work, we show that simple masked discrete diffusion is more performant than previously thought. We apply an effective training recipe that improves the performance of masked diffusion models and derive a simplified, Rao-Blackwellized objective that results in additional improvements. Our objective has a simple form -- it is a mixture of classical masked language modeling losses -- and can be used to train encoder-only language models that admit efficient samplers, including ones that can generate arbitrary lengths of text semi-autoregressively like a traditional language model. On language modeling benchmarks, a range of masked diffusion models trained with modern engineering practices achieves a new state-of-the-art among diffusion models, and approaches AR perplexity. We release our code at: https://github.com/kuleshov-group/mdlm

We present Diffusion Model Patching (DMP), a simple method to boost the performance of pre-trained diffusion models that have already reached convergence, with a negligible increase in parameters. DMP inserts a small, learnable set of prompts into the model's input space while keeping the original model frozen. The effectiveness of DMP is not merely due to the addition of parameters but stems from its dynamic gating mechanism, which selects and combines a subset of learnable prompts at every step of the generative process (e.g., reverse denoising steps). This strategy, which we term "mixture-of-prompts", enables the model to draw on the distinct expertise of each prompt, essentially "patching" the model's functionality at every step with minimal yet specialized parameters. Uniquely, DMP enhances the model by further training on the same dataset on which it was originally trained, even in a scenario where significant improvements are typically not expected due to model convergence. Experiments show that DMP significantly enhances the converged FID of DiT-L/2 on FFHQ 256x256 by 10.38%, achieved with only a 1.43% parameter increase and 50K additional training iterations.

Diffusion models have exhibited remarkable capabilities in text-to-image generation. However, their performance in image-to-text generation, specifically image captioning, has lagged behind Auto-Regressive (AR) models, casting doubt on their applicability for such tasks. In this work, we revisit diffusion models, highlighting their capacity for holistic context modeling and parallel decoding. With these benefits, diffusion models can alleviate the inherent limitations of AR methods, including their slow inference speed, error propagation, and unidirectional constraints. Furthermore, we identify the prior underperformance of diffusion models stemming from the absence of an effective latent space for image-text alignment, and the discrepancy between continuous diffusion processes and discrete textual data. In response, we introduce a novel architecture, LaDiC, which utilizes a split BERT to create a dedicated latent space for captions and integrates a regularization module to manage varying text lengths. Our framework also includes a diffuser for semantic image-to-text conversion and a Back&Refine technique to enhance token interactivity during inference. LaDiC achieves state-of-the-art performance for diffusion-based methods on the MS COCO dataset with 38.2 BLEU@4 and 126.2 CIDEr, demonstrating exceptional performance without pre-training or ancillary modules. This indicates strong competitiveness with AR models, revealing the previously untapped potential of diffusion models in image-to-text generation.

Recent empirical studies have demonstrated that diffusion models can effectively learn the image distribution and generate new samples. Remarkably, these models can achieve this even with a small number of training samples despite a large image dimension, circumventing the curse of dimensionality. In this work, we provide theoretical insights into this phenomenon by leveraging key empirical observations: (i) the low intrinsic dimensionality of image data, (ii) a union of manifold structure of image data, and (iii) the low-rank property of the denoising autoencoder in trained diffusion models. These observations motivate us to assume the underlying data distribution of image data as a mixture of low-rank Gaussians and to parameterize the denoising autoencoder as a low-rank model according to the score function of the assumed distribution. With these setups, we rigorously show that optimizing the training loss of diffusion models is equivalent to solving the canonical subspace clustering problem over the training samples. Based on this equivalence, we further show that the minimal number of samples required to learn the underlying distribution scales linearly with the intrinsic dimensions under the above data and model assumptions. This insight sheds light on why diffusion models can break the curse of dimensionality and exhibit the phase transition in learning distributions. Moreover, we empirically establish a correspondence between the subspaces and the semantic representations of image data, facilitating image editing. We validate these results with corroborated experimental results on both simulated distributions and image datasets.

Diffusion Models (DMs) have exhibited superior performance in generating high-quality and diverse images. However, this exceptional performance comes at the cost of expensive architectural design, particularly due to the attention module heavily used in leading models. Existing works mainly adopt a retraining process to enhance DM efficiency. This is computationally expensive and not very scalable. To this end, we introduce the Attention-driven Training-free Efficient Diffusion Model (AT-EDM) framework that leverages attention maps to perform run-time pruning of redundant tokens, without the need for any retraining. Specifically, for single-denoising-step pruning, we develop a novel ranking algorithm, Generalized Weighted Page Rank (G-WPR), to identify redundant tokens, and a similarity-based recovery method to restore tokens for the convolution operation. In addition, we propose a Denoising-Steps-Aware Pruning (DSAP) approach to adjust the pruning budget across different denoising timesteps for better generation quality. Extensive evaluations show that AT-EDM performs favorably against prior art in terms of efficiency (e.g., 38.8% FLOPs saving and up to 1.53x speed-up over Stable Diffusion XL) while maintaining nearly the same FID and CLIP scores as the full model. Project webpage: https://atedm.github.io.

As one of the most popular and sought-after generative models in the recent years, diffusion models have sparked the interests of many researchers and steadily shown excellent advantage in various generative tasks such as image synthesis, video generation, molecule design, 3D scene rendering and multimodal generation, relying on their dense theoretical principles and reliable application practices. The remarkable success of these recent efforts on diffusion models comes largely from progressive design principles and efficient architecture, training, inference, and deployment methodologies. However, there has not been a comprehensive and in-depth review to summarize these principles and practices to help the rapid understanding and application of diffusion models. In this survey, we provide a new efficiency-oriented perspective on these existing efforts, which mainly focuses on the profound principles and efficient practices in architecture designs, model training, fast inference and reliable deployment, to guide further theoretical research, algorithm migration and model application for new scenarios in a reader-friendly way. https://github.com/ponyzym/Efficient-DMs-Survey

Diffusion-based generative modeling has been achieving state-of-the-art results on various generation tasks. Most diffusion models, however, are limited to a single-generation modeling. Can we generalize diffusion models with the ability of multi-modal generative training for more generalizable modeling? In this paper, we propose a principled way to define a diffusion model by constructing a unified multi-modal diffusion model in a common diffusion space. We define the forward diffusion process to be driven by an information aggregation from multiple types of task-data, e.g., images for a generation task and labels for a classification task. In the reverse process, we enforce information sharing by parameterizing a shared backbone denoising network with additional modality-specific decoder heads. Such a structure can simultaneously learn to generate different types of multi-modal data with a multi-task loss, which is derived from a new multi-modal variational lower bound that generalizes the standard diffusion model. We propose several multimodal generation settings to verify our framework, including image transition, masked-image training, joint image-label and joint image-representation generative modeling. Extensive experimental results on ImageNet indicate the effectiveness of our framework for various multi-modal generative modeling, which we believe is an important research direction worthy of more future explorations.

Masked diffusion models (MDMs) have emerged as a popular research topic for generative modeling of discrete data, thanks to their superior performance over other discrete diffusion models, and are rivaling the auto-regressive models (ARMs) for language modeling tasks. The recent effort in simplifying the masked diffusion framework further leads to alignment with continuous-space diffusion models and more principled training and sampling recipes. In this paper, however, we reveal that both training and sampling of MDMs are theoretically free from the time variable, arguably the key signature of diffusion models, and are instead equivalent to masked models. The connection on the sampling aspect is drawn by our proposed first-hitting sampler (FHS). Specifically, we show that the FHS is theoretically equivalent to MDMs' original generation process while significantly alleviating the time-consuming categorical sampling and achieving a 20times speedup. In addition, our investigation raises doubts about whether MDMs can truly beat ARMs. We identify, for the first time, an underlying numerical issue, even with the commonly used 32-bit floating-point precision, which results in inaccurate categorical sampling. We show that the numerical issue lowers the effective temperature both theoretically and empirically, and the resulting decrease in token diversity makes previous evaluations, which assess the generation quality solely through the incomplete generative perplexity metric, somewhat unfair.

Diffusion models have become a popular approach for image generation and reconstruction due to their numerous advantages. However, most diffusion-based inverse problem-solving methods only deal with 2D images, and even recently published 3D methods do not fully exploit the 3D distribution prior. To address this, we propose a novel approach using two perpendicular pre-trained 2D diffusion models to solve the 3D inverse problem. By modeling the 3D data distribution as a product of 2D distributions sliced in different directions, our method effectively addresses the curse of dimensionality. Our experimental results demonstrate that our method is highly effective for 3D medical image reconstruction tasks, including MRI Z-axis super-resolution, compressed sensing MRI, and sparse-view CT. Our method can generate high-quality voxel volumes suitable for medical applications.

Generating photos satisfying multiple constraints find broad utility in the content creation industry. A key hurdle to accomplishing this task is the need for paired data consisting of all modalities (i.e., constraints) and their corresponding output. Moreover, existing methods need retraining using paired data across all modalities to introduce a new condition. This paper proposes a solution to this problem based on denoising diffusion probabilistic models (DDPMs). Our motivation for choosing diffusion models over other generative models comes from the flexible internal structure of diffusion models. Since each sampling step in the DDPM follows a Gaussian distribution, we show that there exists a closed-form solution for generating an image given various constraints. Our method can unite multiple diffusion models trained on multiple sub-tasks and conquer the combined task through our proposed sampling strategy. We also introduce a novel reliability parameter that allows using different off-the-shelf diffusion models trained across various datasets during sampling time alone to guide it to the desired outcome satisfying multiple constraints. We perform experiments on various standard multimodal tasks to demonstrate the effectiveness of our approach. More details can be found in https://nithin-gk.github.io/projectpages/Multidiff/index.html

Large language models (LLMs) are fine-tuned using human comparison data with Reinforcement Learning from Human Feedback (RLHF) methods to make them better aligned with users' preferences. In contrast to LLMs, human preference learning has not been widely explored in text-to-image diffusion models; the best existing approach is to fine-tune a pretrained model using carefully curated high quality images and captions to improve visual appeal and text alignment. We propose Diffusion-DPO, a method to align diffusion models to human preferences by directly optimizing on human comparison data. Diffusion-DPO is adapted from the recently developed Direct Preference Optimization (DPO), a simpler alternative to RLHF which directly optimizes a policy that best satisfies human preferences under a classification objective. We re-formulate DPO to account for a diffusion model notion of likelihood, utilizing the evidence lower bound to derive a differentiable objective. Using the Pick-a-Pic dataset of 851K crowdsourced pairwise preferences, we fine-tune the base model of the state-of-the-art Stable Diffusion XL (SDXL)-1.0 model with Diffusion-DPO. Our fine-tuned base model significantly outperforms both base SDXL-1.0 and the larger SDXL-1.0 model consisting of an additional refinement model in human evaluation, improving visual appeal and prompt alignment. We also develop a variant that uses AI feedback and has comparable performance to training on human preferences, opening the door for scaling of diffusion model alignment methods.

Recently, diffusion probabilistic models (DPMs) have achieved promising results in diverse generative tasks. A typical DPM framework includes a forward process that gradually diffuses the data distribution and a reverse process that recovers the data distribution from time-dependent data scores. In this work, we observe that the stochastic reverse process of data scores is a martingale, from which concentration bounds and the optional stopping theorem for data scores can be derived. Then, we discover a simple way for calibrating an arbitrary pretrained DPM, with which the score matching loss can be reduced and the lower bounds of model likelihood can consequently be increased. We provide general calibration guidelines under various model parametrizations. Our calibration method is performed only once and the resulting models can be used repeatedly for sampling. We conduct experiments on multiple datasets to empirically validate our proposal. Our code is at https://github.com/thudzj/Calibrated-DPMs.

World models constitute a promising approach for training reinforcement learning agents in a safe and sample-efficient manner. Recent world models predominantly operate on sequences of discrete latent variables to model environment dynamics. However, this compression into a compact discrete representation may ignore visual details that are important for reinforcement learning. Concurrently, diffusion models have become a dominant approach for image generation, challenging well-established methods modeling discrete latents. Motivated by this paradigm shift, we introduce DIAMOND (DIffusion As a Model Of eNvironment Dreams), a reinforcement learning agent trained in a diffusion world model. We analyze the key design choices that are required to make diffusion suitable for world modeling, and demonstrate how improved visual details can lead to improved agent performance. DIAMOND achieves a mean human normalized score of 1.46 on the competitive Atari 100k benchmark; a new best for agents trained entirely within a world model. To foster future research on diffusion for world modeling, we release our code, agents and playable world models at https://github.com/eloialonso/diamond.

In recent years, image generation has shown a great leap in performance, where diffusion models play a central role. Although generating high-quality images, such models are mainly conditioned on textual descriptions. This begs the question: "how can we adopt such models to be conditioned on other modalities?". In this paper, we propose a novel method utilizing latent diffusion models trained for text-to-image-generation to generate images conditioned on audio recordings. Using a pre-trained audio encoding model, the proposed method encodes audio into a new token, which can be considered as an adaptation layer between the audio and text representations. Such a modeling paradigm requires a small number of trainable parameters, making the proposed approach appealing for lightweight optimization. Results suggest the proposed method is superior to the evaluated baseline methods, considering objective and subjective metrics. Code and samples are available at: https://pages.cs.huji.ac.il/adiyoss-lab/AudioToken.

Part of the success of diffusion models stems from their ability to perform iterative refinement, i.e., repeatedly correcting outputs during generation. However, modern masked discrete diffusion lacks this capability: when a token is generated, it cannot be updated again, even when it introduces an error. Here, we address this limitation by introducing the remasking diffusion model (ReMDM) sampler, a method that can be applied to pretrained masked diffusion models in a principled way and that is derived from a discrete diffusion model with a custom remasking backward process. Most interestingly, ReMDM endows discrete diffusion with a form of inference-time compute scaling. By increasing the number of sampling steps, ReMDM generates natural language outputs that approach the quality of autoregressive models, whereas when the computation budget is limited, ReMDM better maintains quality. ReMDM also improves sample quality of masked diffusion models for discretized images, and in scientific domains such as molecule design, ReMDM facilitates diffusion guidance and pushes the Pareto frontier of controllability relative to classical masking and uniform noise diffusion. We provide the code along with a blog post on the project page: https://remdm.github.io.

Score-based diffusion models, while achieving remarkable empirical performance, often suffer from low sampling speed, due to extensive function evaluations needed during the sampling phase. Despite a flurry of recent activities towards speeding up diffusion generative modeling in practice, theoretical underpinnings for acceleration techniques remain severely limited. In this paper, we design novel training-free algorithms to accelerate popular deterministic (i.e., DDIM) and stochastic (i.e., DDPM) samplers. Our accelerated deterministic sampler converges at a rate O(1/{T}^2) with T the number of steps, improving upon the O(1/T) rate for the DDIM sampler; and our accelerated stochastic sampler converges at a rate O(1/T), outperforming the rate O(1/T) for the DDPM sampler. The design of our algorithms leverages insights from higher-order approximation, and shares similar intuitions as popular high-order ODE solvers like the DPM-Solver-2. Our theory accommodates ell_2-accurate score estimates, and does not require log-concavity or smoothness on the target distribution.

Diffusion models have emerged as a formidable tool for training-free conditional generation.However, a key hurdle in inference-time guidance techniques is the need for compute-heavy backpropagation through the diffusion network for estimating the guidance direction. Moreover, these techniques often require handcrafted parameter tuning on a case-by-case basis. Although some recent works have introduced minimal compute methods for linear inverse problems, a generic lightweight guidance solution to both linear and non-linear guidance problems is still missing. To this end, we propose Dreamguider, a method that enables inference-time guidance without compute-heavy backpropagation through the diffusion network. The key idea is to regulate the gradient flow through a time-varying factor. Moreover, we propose an empirical guidance scale that works for a wide variety of tasks, hence removing the need for handcrafted parameter tuning. We further introduce an effective lightweight augmentation strategy that significantly boosts the performance during inference-time guidance. We present experiments using Dreamguider on multiple tasks across multiple datasets and models to show the effectiveness of the proposed modules. To facilitate further research, we will make the code public after the review process.

Typical generative diffusion models rely on a Gaussian diffusion process for training the backward transformations, which can then be used to generate samples from Gaussian noise. However, real world data often takes place in discrete-state spaces, including many scientific applications. Here, we develop a theoretical formulation for arbitrary discrete-state Markov processes in the forward diffusion process using exact (as opposed to variational) analysis. We relate the theory to the existing continuous-state Gaussian diffusion as well as other approaches to discrete diffusion, and identify the corresponding reverse-time stochastic process and score function in the continuous-time setting, and the reverse-time mapping in the discrete-time setting. As an example of this framework, we introduce ``Blackout Diffusion'', which learns to produce samples from an empty image instead of from noise. Numerical experiments on the CIFAR-10, Binarized MNIST, and CelebA datasets confirm the feasibility of our approach. Generalizing from specific (Gaussian) forward processes to discrete-state processes without a variational approximation sheds light on how to interpret diffusion models, which we discuss.

Diffusion probabilistic models (DPMs) have achieved impressive success in high-resolution image synthesis, especially in recent large-scale text-to-image generation applications. An essential technique for improving the sample quality of DPMs is guided sampling, which usually needs a large guidance scale to obtain the best sample quality. The commonly-used fast sampler for guided sampling is DDIM, a first-order diffusion ODE solver that generally needs 100 to 250 steps for high-quality samples. Although recent works propose dedicated high-order solvers and achieve a further speedup for sampling without guidance, their effectiveness for guided sampling has not been well-tested before. In this work, we demonstrate that previous high-order fast samplers suffer from instability issues, and they even become slower than DDIM when the guidance scale grows large. To further speed up guided sampling, we propose DPM-Solver++, a high-order solver for the guided sampling of DPMs. DPM-Solver++ solves the diffusion ODE with the data prediction model and adopts thresholding methods to keep the solution matches training data distribution. We further propose a multistep variant of DPM-Solver++ to address the instability issue by reducing the effective step size. Experiments show that DPM-Solver++ can generate high-quality samples within only 15 to 20 steps for guided sampling by pixel-space and latent-space DPMs.

Diffusion models are proficient at generating high-quality images. They are however effective only when operating at the resolution used during training. Inference at a scaled resolution leads to repetitive patterns and structural distortions. Retraining at higher resolutions quickly becomes prohibitive. Thus, methods enabling pre-existing diffusion models to operate at flexible test-time resolutions are highly desirable. Previous works suffer from frequent artifacts and often introduce large latency overheads. We propose two simple modules that combine to solve these issues. We introduce a Frequency Modulation (FM) module that leverages the Fourier domain to improve the global structure consistency, and an Attention Modulation (AM) module which improves the consistency of local texture patterns, a problem largely ignored in prior works. Our method, coined Fam diffusion, can seamlessly integrate into any latent diffusion model and requires no additional training. Extensive qualitative results highlight the effectiveness of our method in addressing structural and local artifacts, while quantitative results show state-of-the-art performance. Also, our method avoids redundant inference tricks for improved consistency such as patch-based or progressive generation, leading to negligible latency overheads.

Diffusion models (DMs) demonstrate potent image generation capabilities in various generative modeling tasks. Nevertheless, their primary limitation lies in slow sampling speed, requiring hundreds or thousands of sequential function evaluations through large neural networks to generate high-quality images. Sampling from DMs can be seen alternatively as solving corresponding stochastic differential equations (SDEs) or ordinary differential equations (ODEs). In this work, we formulate the sampling process as an extended reverse-time SDE (ER SDE), unifying prior explorations into ODEs and SDEs. Leveraging the semi-linear structure of ER SDE solutions, we offer exact solutions and arbitrarily high-order approximate solutions for VP SDE and VE SDE, respectively. Based on the solution space of the ER SDE, we yield mathematical insights elucidating the superior performance of ODE solvers over SDE solvers in terms of fast sampling. Additionally, we unveil that VP SDE solvers stand on par with their VE SDE counterparts. Finally, we devise fast and training-free samplers, ER-SDE-Solvers, achieving state-of-the-art performance across all stochastic samplers. Experimental results demonstrate achieving 3.45 FID in 20 function evaluations and 2.24 FID in 50 function evaluations on the ImageNet 64times64 dataset.

Denoising Diffusion Probabilistic Models (DDPMs) have garnered popularity for data generation across various domains. However, a significant bottleneck is the necessity for whole-network computation during every step of the generative process, leading to high computational overheads. This paper presents a novel framework, Denoising Diffusion Step-aware Models (DDSM), to address this challenge. Unlike conventional approaches, DDSM employs a spectrum of neural networks whose sizes are adapted according to the importance of each generative step, as determined through evolutionary search. This step-wise network variation effectively circumvents redundant computational efforts, particularly in less critical steps, thereby enhancing the efficiency of the diffusion model. Furthermore, the step-aware design can be seamlessly integrated with other efficiency-geared diffusion models such as DDIMs and latent diffusion, thus broadening the scope of computational savings. Empirical evaluations demonstrate that DDSM achieves computational savings of 49% for CIFAR-10, 61% for CelebA-HQ, 59% for LSUN-bedroom, 71% for AFHQ, and 76% for ImageNet, all without compromising the generation quality. Our code and models will be publicly available.

Score-based diffusion models learn to reverse a stochastic differential equation that maps data to noise. However, for complex tasks, numerical error can compound and result in highly unnatural samples. Previous work mitigates this drift with thresholding, which projects to the natural data domain (such as pixel space for images) after each diffusion step, but this leads to a mismatch between the training and generative processes. To incorporate data constraints in a principled manner, we present Reflected Diffusion Models, which instead reverse a reflected stochastic differential equation evolving on the support of the data. Our approach learns the perturbed score function through a generalized score matching loss and extends key components of standard diffusion models including diffusion guidance, likelihood-based training, and ODE sampling. We also bridge the theoretical gap with thresholding: such schemes are just discretizations of reflected SDEs. On standard image benchmarks, our method is competitive with or surpasses the state of the art without architectural modifications and, for classifier-free guidance, our approach enables fast exact sampling with ODEs and produces more faithful samples under high guidance weight.

Diffusion models currently dominate the field of data-driven image synthesis with their unparalleled scaling to large datasets. In this paper, we identify and rectify several causes for uneven and ineffective training in the popular ADM diffusion model architecture, without altering its high-level structure. Observing uncontrolled magnitude changes and imbalances in both the network activations and weights over the course of training, we redesign the network layers to preserve activation, weight, and update magnitudes on expectation. We find that systematic application of this philosophy eliminates the observed drifts and imbalances, resulting in considerably better networks at equal computational complexity. Our modifications improve the previous record FID of 2.41 in ImageNet-512 synthesis to 1.81, achieved using fast deterministic sampling. As an independent contribution, we present a method for setting the exponential moving average (EMA) parameters post-hoc, i.e., after completing the training run. This allows precise tuning of EMA length without the cost of performing several training runs, and reveals its surprising interactions with network architecture, training time, and guidance.

Diffusion models have been used extensively for high quality image and video generation tasks. In this paper, we propose a novel conditional diffusion model with spatial attention and latent embedding (cDAL) for medical image segmentation. In cDAL, a convolutional neural network (CNN) based discriminator is used at every time-step of the diffusion process to distinguish between the generated labels and the real ones. A spatial attention map is computed based on the features learned by the discriminator to help cDAL generate more accurate segmentation of discriminative regions in an input image. Additionally, we incorporated a random latent embedding into each layer of our model to significantly reduce the number of training and sampling time-steps, thereby making it much faster than other diffusion models for image segmentation. We applied cDAL on 3 publicly available medical image segmentation datasets (MoNuSeg, Chest X-ray and Hippocampus) and observed significant qualitative and quantitative improvements with higher Dice scores and mIoU over the state-of-the-art algorithms. The source code is publicly available at https://github.com/Hejrati/cDAL/.

Score-based diffusion models have emerged as one of the most promising frameworks for deep generative modelling, due to their state-of-the art performance in many generation tasks while relying on mathematical foundations such as stochastic differential equations (SDEs) and ordinary differential equations (ODEs). Empirically, it has been reported that ODE based samples are inferior to SDE based samples. In this paper we rigorously describe the range of dynamics and approximations that arise when training score-based diffusion models, including the true SDE dynamics, the neural approximations, the various approximate particle dynamics that result, as well as their associated Fokker--Planck equations and the neural network approximations of these Fokker--Planck equations. We systematically analyse the difference between the ODE and SDE dynamics of score-based diffusion models, and link it to an associated Fokker--Planck equation. We derive a theoretical upper bound on the Wasserstein 2-distance between the ODE- and SDE-induced distributions in terms of a Fokker--Planck residual. We also show numerically that conventional score-based diffusion models can exhibit significant differences between ODE- and SDE-induced distributions which we demonstrate using explicit comparisons. Moreover, we show numerically that reducing the Fokker--Planck residual by adding it as an additional regularisation term leads to closing the gap between ODE- and SDE-induced distributions. Our experiments suggest that this regularisation can improve the distribution generated by the ODE, however that this can come at the cost of degraded SDE sample quality.

While many unsupervised learning models focus on one family of tasks, either generative or discriminative, we explore the possibility of a unified representation learner: a model which addresses both families of tasks simultaneously. We identify diffusion models, a state-of-the-art method for generative tasks, as a prime candidate. Such models involve training a U-Net to iteratively predict and remove noise, and the resulting model can synthesize high-fidelity, diverse, novel images. We find that the intermediate feature maps of the U-Net are diverse, discriminative feature representations. We propose a novel attention mechanism for pooling feature maps and further leverage this mechanism as DifFormer, a transformer feature fusion of features from different diffusion U-Net blocks and noise steps. We also develop DifFeed, a novel feedback mechanism tailored to diffusion. We find that diffusion models are better than GANs, and, with our fusion and feedback mechanisms, can compete with state-of-the-art unsupervised image representation learning methods for discriminative tasks - image classification with full and semi-supervision, transfer for fine-grained classification, object detection and segmentation, and semantic segmentation. Our project website (https://mgwillia.github.io/diffssl/) and code (https://github.com/soumik-kanad/diffssl) are available publicly.

Recent studies indicate that the denoising process in deep generative diffusion models implicitly learns and memorizes semantic information from the data distribution. These findings suggest that capturing more complex data distributions requires larger neural networks, leading to a substantial increase in computational demands, which in turn become the primary bottleneck in both training and inference of diffusion models. To this end, we introduce Generative Modeling with Explicit Memory (GMem), leveraging an external memory bank in both training and sampling phases of diffusion models. This approach preserves semantic information from data distributions, reducing reliance on neural network capacity for learning and generalizing across diverse datasets. The results are significant: our GMem enhances both training, sampling efficiency, and generation quality. For instance, on ImageNet at 256 times 256 resolution, GMem accelerates SiT training by over 46.7times, achieving the performance of a SiT model trained for 7M steps in fewer than 150K steps. Compared to the most efficient existing method, REPA, GMem still offers a 16times speedup, attaining an FID score of 5.75 within 250K steps, whereas REPA requires over 4M steps. Additionally, our method achieves state-of-the-art generation quality, with an FID score of {3.56} without classifier-free guidance on ImageNet 256times256. Our code is available at https://github.com/LINs-lab/GMem.

Diffusion models have emerged as a key pillar of foundation models in visual domains. One of their critical applications is to universally solve different downstream inverse tasks via a single diffusion prior without re-training for each task. Most inverse tasks can be formulated as inferring a posterior distribution over data (e.g., a full image) given a measurement (e.g., a masked image). This is however challenging in diffusion models since the nonlinear and iterative nature of the diffusion process renders the posterior intractable. To cope with this challenge, we propose a variational approach that by design seeks to approximate the true posterior distribution. We show that our approach naturally leads to regularization by denoising diffusion process (RED-Diff) where denoisers at different timesteps concurrently impose different structural constraints over the image. To gauge the contribution of denoisers from different timesteps, we propose a weighting mechanism based on signal-to-noise-ratio (SNR). Our approach provides a new variational perspective for solving inverse problems with diffusion models, allowing us to formulate sampling as stochastic optimization, where one can simply apply off-the-shelf solvers with lightweight iterates. Our experiments for image restoration tasks such as inpainting and superresolution demonstrate the strengths of our method compared with state-of-the-art sampling-based diffusion models.

As a class of fruitful approaches, diffusion probabilistic models (DPMs) have shown excellent advantages in high-resolution image reconstruction. On the other hand, masked autoencoders (MAEs), as popular self-supervised vision learners, have demonstrated simpler and more effective image reconstruction and transfer capabilities on downstream tasks. However, they all require extremely high training costs, either due to inherent high temporal-dependence (i.e., excessively long diffusion steps) or due to artificially low spatial-dependence (i.e., human-formulated high mask ratio, such as 0.75). To the end, this paper presents LMD, a faster image reconstruction framework with latent masking diffusion. First, we propose to project and reconstruct images in latent space through a pre-trained variational autoencoder, which is theoretically more efficient than in the pixel-based space. Then, we combine the advantages of MAEs and DPMs to design a progressive masking diffusion model, which gradually increases the masking proportion by three different schedulers and reconstructs the latent features from simple to difficult, without sequentially performing denoising diffusion as in DPMs or using fixed high masking ratio as in MAEs, so as to alleviate the high training time-consumption predicament. Our approach allows for learning high-capacity models and accelerate their training (by 3x or more) and barely reduces the original accuracy. Inference speed in downstream tasks also significantly outperforms the previous approaches.

Being the most cutting-edge generative methods, diffusion methods have shown great advances in wide generation tasks. Among them, graph generation attracts significant research attention for its broad application in real life. In our survey, we systematically and comprehensively review on diffusion-based graph generative methods. We first make a review on three mainstream paradigms of diffusion methods, which are denoising diffusion probabilistic models, score-based genrative models, and stochastic differential equations. Then we further categorize and introduce the latest applications of diffusion models on graphs. In the end, we point out some limitations of current studies and future directions of future explorations. The summary of existing methods metioned in this survey is in https://github.com/zhejiangzhuque/Diffusion-based-Graph-Generative-Methods.

Consistency Models (CM) (Song et al., 2023) accelerate score-based diffusion model sampling at the cost of sample quality but lack a natural way to trade-off quality for speed. To address this limitation, we propose Consistency Trajectory Model (CTM), a generalization encompassing CM and score-based models as special cases. CTM trains a single neural network that can -- in a single forward pass -- output scores (i.e., gradients of log-density) and enables unrestricted traversal between any initial and final time along the Probability Flow Ordinary Differential Equation (ODE) in a diffusion process. CTM enables the efficient combination of adversarial training and denoising score matching loss to enhance performance and achieves new state-of-the-art FIDs for single-step diffusion model sampling on CIFAR-10 (FID 1.73) and ImageNet at 64x64 resolution (FID 1.92). CTM also enables a new family of sampling schemes, both deterministic and stochastic, involving long jumps along the ODE solution trajectories. It consistently improves sample quality as computational budgets increase, avoiding the degradation seen in CM. Furthermore, unlike CM, CTM's access to the score function can streamline the adoption of established controllable/conditional generation methods from the diffusion community. This access also enables the computation of likelihood. The code is available at https://github.com/sony/ctm.

We derive a minimalist but powerful deterministic denoising-diffusion model. While denoising diffusion has shown great success in many domains, its underlying theory remains largely inaccessible to non-expert users. Indeed, an understanding of graduate-level concepts such as Langevin dynamics or score matching appears to be required to grasp how it works. We propose an alternative approach that requires no more than undergrad calculus and probability. We consider two densities and observe what happens when random samples from these densities are blended (linearly interpolated). We show that iteratively blending and deblending samples produces random paths between the two densities that converge toward a deterministic mapping. This mapping can be evaluated with a neural network trained to deblend samples. We obtain a model that behaves like deterministic denoising diffusion: it iteratively maps samples from one density (e.g., Gaussian noise) to another (e.g., cat images). However, compared to the state-of-the-art alternative, our model is simpler to derive, simpler to implement, more numerically stable, achieves higher quality results in our experiments, and has interesting connections to computer graphics.

In a convergence of machine learning and biology, we reveal that diffusion models are evolutionary algorithms. By considering evolution as a denoising process and reversed evolution as diffusion, we mathematically demonstrate that diffusion models inherently perform evolutionary algorithms, naturally encompassing selection, mutation, and reproductive isolation. Building on this equivalence, we propose the Diffusion Evolution method: an evolutionary algorithm utilizing iterative denoising -- as originally introduced in the context of diffusion models -- to heuristically refine solutions in parameter spaces. Unlike traditional approaches, Diffusion Evolution efficiently identifies multiple optimal solutions and outperforms prominent mainstream evolutionary algorithms. Furthermore, leveraging advanced concepts from diffusion models, namely latent space diffusion and accelerated sampling, we introduce Latent Space Diffusion Evolution, which finds solutions for evolutionary tasks in high-dimensional complex parameter space while significantly reducing computational steps. This parallel between diffusion and evolution not only bridges two different fields but also opens new avenues for mutual enhancement, raising questions about open-ended evolution and potentially utilizing non-Gaussian or discrete diffusion models in the context of Diffusion Evolution.

We propose a novel family of language models, Latent-Thought Language Models (LTMs), which incorporate explicit latent thought vectors that follow an explicit prior model in latent space. These latent thought vectors guide the autoregressive generation of ground tokens through a Transformer decoder. Training employs a dual-rate optimization process within the classical variational Bayes framework: fast learning of local variational parameters for the posterior distribution of latent vectors, and slow learning of global decoder parameters. Empirical studies reveal that LTMs possess additional scaling dimensions beyond traditional LLMs, yielding a structured design space. Higher sample efficiency can be achieved by increasing training compute per token, with further gains possible by trading model size for more inference steps. Designed based on these scaling properties, LTMs demonstrate superior sample and parameter efficiency compared to conventional autoregressive models and discrete diffusion models. They significantly outperform these counterparts in validation perplexity and zero-shot language modeling. Additionally, LTMs exhibit emergent few-shot in-context reasoning capabilities that scale with model and latent size, and achieve competitive performance in conditional and unconditional text generation.

Typical diffusion models are trained to accept a particular form of conditioning, most commonly text, and cannot be conditioned on other modalities without retraining. In this work, we propose a universal guidance algorithm that enables diffusion models to be controlled by arbitrary guidance modalities without the need to retrain any use-specific components. We show that our algorithm successfully generates quality images with guidance functions including segmentation, face recognition, object detection, and classifier signals. Code is available at https://github.com/arpitbansal297/Universal-Guided-Diffusion.

Despite a growing interest in diffusion-based language models, existing work has not shown that these models can attain nontrivial likelihoods on standard language modeling benchmarks. In this work, we take the first steps towards closing the likelihood gap between autoregressive and diffusion-based language models, with the goal of building and releasing a diffusion model which outperforms a small but widely-known autoregressive model. We pursue this goal through algorithmic improvements, scaling laws, and increased compute. On the algorithmic front, we introduce several methodological improvements for the maximum-likelihood training of diffusion language models. We then study scaling laws for our diffusion models and find compute-optimal training regimes which differ substantially from autoregressive models. Using our methods and scaling analysis, we train and release Plaid 1B, a large diffusion language model which outperforms GPT-2 124M in likelihood on benchmark datasets and generates fluent samples in unconditional and zero-shot control settings.

Standard diffusion models involve an image transform -- adding Gaussian noise -- and an image restoration operator that inverts this degradation. We observe that the generative behavior of diffusion models is not strongly dependent on the choice of image degradation, and in fact an entire family of generative models can be constructed by varying this choice. Even when using completely deterministic degradations (e.g., blur, masking, and more), the training and test-time update rules that underlie diffusion models can be easily generalized to create generative models. The success of these fully deterministic models calls into question the community's understanding of diffusion models, which relies on noise in either gradient Langevin dynamics or variational inference, and paves the way for generalized diffusion models that invert arbitrary processes. Our code is available at https://github.com/arpitbansal297/Cold-Diffusion-Models

We present high quality image synthesis results using diffusion probabilistic models, a class of latent variable models inspired by considerations from nonequilibrium thermodynamics. Our best results are obtained by training on a weighted variational bound designed according to a novel connection between diffusion probabilistic models and denoising score matching with Langevin dynamics, and our models naturally admit a progressive lossy decompression scheme that can be interpreted as a generalization of autoregressive decoding. On the unconditional CIFAR10 dataset, we obtain an Inception score of 9.46 and a state-of-the-art FID score of 3.17. On 256x256 LSUN, we obtain sample quality similar to ProgressiveGAN. Our implementation is available at https://github.com/hojonathanho/diffusion

Autoregressive models for text sometimes generate repetitive and low-quality output because errors accumulate during the steps of generation. This issue is often attributed to exposure bias - the difference between how a model is trained, and how it is used during inference. Denoising diffusion models provide an alternative approach in which a model can revisit and revise its output. However, they can be computationally expensive and prior efforts on text have led to models that produce less fluent output compared to autoregressive models, especially for longer text and paragraphs. In this paper, we propose PLANNER, a model that combines latent semantic diffusion with autoregressive generation, to generate fluent text while exercising global control over paragraphs. The model achieves this by combining an autoregressive "decoding" module with a "planning" module that uses latent diffusion to generate semantic paragraph embeddings in a coarse-to-fine manner. The proposed method is evaluated on various conditional generation tasks, and results on semantic generation, text completion and summarization show its effectiveness in generating high-quality long-form text in an efficient manner.

Diffusion Probabilistic Models (DPM) have shown remarkable efficacy in the synthesis of high-quality images. However, their inference process characteristically requires numerous, potentially hundreds, of iterative steps, which could exaggerate the problem of exposure bias due to the training and inference discrepancy. Previous work has attempted to mitigate this issue by perturbing inputs during training, which consequently mandates the retraining of the DPM. In this work, we conduct a systematic study of exposure bias in DPM and, intriguingly, we find that the exposure bias could be alleviated with a novel sampling method that we propose, without retraining the model. We empirically and theoretically show that, during inference, for each backward time step t and corresponding state x_t, there might exist another time step t_s which exhibits superior coupling with x_t. Based on this finding, we introduce a sampling method named Time-Shift Sampler. Our framework can be seamlessly integrated to existing sampling algorithms, such as DDPM, DDIM and other high-order solvers, inducing merely minimal additional computations. Experimental results show our method brings significant and consistent improvements in FID scores on different datasets and sampling methods. For example, integrating Time-Shift Sampler to F-PNDM yields a FID=3.88, achieving 44.49\% improvements as compared to F-PNDM, on CIFAR-10 with 10 sampling steps, which is more performant than the vanilla DDIM with 100 sampling steps. Our code is available at https://github.com/Mingxiao-Li/TS-DPM.

Diffusion models have significantly advanced the state of the art in image, audio, and video generation tasks. However, their applications in practical scenarios are hindered by slow inference speed. Drawing inspiration from the approximation strategies utilized in consistency models, we propose the Sub-path Linear Approximation Model (SLAM), which accelerates diffusion models while maintaining high-quality image generation. SLAM treats the PF-ODE trajectory as a series of PF-ODE sub-paths divided by sampled points, and harnesses sub-path linear (SL) ODEs to form a progressive and continuous error estimation along each individual PF-ODE sub-path. The optimization on such SL-ODEs allows SLAM to construct denoising mappings with smaller cumulative approximated errors. An efficient distillation method is also developed to facilitate the incorporation of more advanced diffusion models, such as latent diffusion models. Our extensive experimental results demonstrate that SLAM achieves an efficient training regimen, requiring only 6 A100 GPU days to produce a high-quality generative model capable of 2 to 4-step generation with high performance. Comprehensive evaluations on LAION, MS COCO 2014, and MS COCO 2017 datasets also illustrate that SLAM surpasses existing acceleration methods in few-step generation tasks, achieving state-of-the-art performance both on FID and the quality of the generated images.