Daily Papers

Pretrained latent diffusion models have shown strong potential for lossy image compression, owing to their powerful generative priors. Most existing diffusion-based methods reconstruct images by iteratively denoising from random noise, guided by compressed latent representations. While these approaches have achieved high reconstruction quality, their multi-step sampling process incurs substantial computational overhead. Moreover, they typically require training separate models for different compression bit-rates, leading to significant training and storage costs. To address these challenges, we propose a one-step diffusion codec across multiple bit-rates. termed OSCAR. Specifically, our method views compressed latents as noisy variants of the original latents, where the level of distortion depends on the bit-rate. This perspective allows them to be modeled as intermediate states along a diffusion trajectory. By establishing a mapping from the compression bit-rate to a pseudo diffusion timestep, we condition a single generative model to support reconstructions at multiple bit-rates. Meanwhile, we argue that the compressed latents retain rich structural information, thereby making one-step denoising feasible. Thus, OSCAR replaces iterative sampling with a single denoising pass, significantly improving inference efficiency. Extensive experiments demonstrate that OSCAR achieves superior performance in both quantitative and visual quality metrics. The code and models will be released at https://github.com/jp-guo/OSCAR.

Diffusion Large Language Models (dLLMs) introduce a new paradigm for language generation, which in turn presents new challenges for aligning them with human preferences. In this work, we aim to improve the policy optimization for dLLMs by reducing the cost of the trajectory probability calculation, thereby enabling scaled-up offline policy training. We prove that: (i) under reference policy regularization, the probability ratio of the newly unmasked tokens is an unbiased estimate of that of intermediate diffusion states, and (ii) the probability of the full trajectory can be effectively estimated with a single forward pass of a re-masked final state. By integrating these two trajectory reduction strategies into a policy optimization objective, we propose Trajectory Reduction Policy Optimization (dTRPO). We evaluate dTRPO on 7B dLLMs across instruction-following and reasoning benchmarks. Results show that it substantially improves the core performance of state-of-the-art dLLMs, achieving gains of up to 9.6% on STEM tasks, up to 4.3% on coding tasks, and up to 3.0% on instruction-following tasks. Moreover, dTRPO exhibits strong training efficiency due to its offline, single-forward nature, and achieves improved generation efficiency through high-quality outputs.

Diffusion priors have been used for blind face restoration (BFR) by fine-tuning diffusion models (DMs) on restoration datasets to recover low-quality images. However, the naive application of DMs presents several key limitations. (i) The diffusion prior has inferior semantic consistency (e.g., ID, structure and color.), increasing the difficulty of optimizing the BFR model; (ii) reliance on hundreds of denoising iterations, preventing the effective cooperation with perceptual losses, which is crucial for faithful restoration. Observing that the latent consistency model (LCM) learns consistency noise-to-data mappings on the ODE-trajectory and therefore shows more semantic consistency in the subject identity, structural information and color preservation, we propose InterLCM to leverage the LCM for its superior semantic consistency and efficiency to counter the above issues. Treating low-quality images as the intermediate state of LCM, InterLCM achieves a balance between fidelity and quality by starting from earlier LCM steps. LCM also allows the integration of perceptual loss during training, leading to improved restoration quality, particularly in real-world scenarios. To mitigate structural and semantic uncertainties, InterLCM incorporates a Visual Module to extract visual features and a Spatial Encoder to capture spatial details, enhancing the fidelity of restored images. Extensive experiments demonstrate that InterLCM outperforms existing approaches in both synthetic and real-world datasets while also achieving faster inference speed.

Diffusion models produce impressive results in modalities ranging from images and video to protein design and text. However, generating samples with user-specified properties remains a challenge. Recent research proposes fine-tuning models to maximize rewards that capture desired properties, but these methods require expensive training and are prone to mode collapse. In this work, we propose Feynman Kac (FK) steering, an inference-time framework for steering diffusion models with reward functions. FK steering works by sampling a system of multiple interacting diffusion processes, called particles, and resampling particles at intermediate steps based on scores computed using functions called potentials. Potentials are defined using rewards for intermediate states and are selected such that a high value indicates that the particle will yield a high-reward sample. We explore various choices of potentials, intermediate rewards, and samplers. We evaluate FK steering on text-to-image and text diffusion models. For steering text-to-image models with a human preference reward, we find that FK steering a 0.8B parameter model outperforms a 2.6B parameter fine-tuned model on prompt fidelity, with faster sampling and no training. For steering text diffusion models with rewards for text quality and specific text attributes, we find that FK steering generates lower perplexity, more linguistically acceptable outputs and enables gradient-free control of attributes like toxicity. Our results demonstrate that inference-time scaling and steering of diffusion models, even with off-the-shelf rewards, can provide significant sample quality gains and controllability benefits. Code is available at https://github.com/zacharyhorvitz/Fk-Diffusion-Steering .

Text-to-image generation using diffusion models has seen explosive popularity owing to their ability in producing high quality images adhering to text prompts. However, production-grade diffusion model serving is a resource intensive task that not only require high-end GPUs which are expensive but also incurs considerable latency. In this paper, we introduce a technique called approximate-caching that can reduce such iterative denoising steps for an image generation based on a prompt by reusing intermediate noise states created during a prior image generation for similar prompts. Based on this idea, we present an end to end text-to-image system, Nirvana, that uses the approximate-caching with a novel cache management-policy Least Computationally Beneficial and Frequently Used (LCBFU) to provide % GPU compute savings, 19.8% end-to-end latency reduction and 19% dollar savings, on average, on two real production workloads. We further present an extensive characterization of real production text-to-image prompts from the perspective of caching, popularity and reuse of intermediate states in a large production environment.

The optimization of the latents and parameters of diffusion models with respect to some differentiable metric defined on the output of the model is a challenging and complex problem. The sampling for diffusion models is done by solving either the probability flow ODE or diffusion SDE wherein a neural network approximates the score function allowing a numerical ODE/SDE solver to be used. However, naive backpropagation techniques are memory intensive, requiring the storage of all intermediate states, and face additional complexity in handling the injected noise from the diffusion term of the diffusion SDE. We propose a novel family of bespoke ODE solvers to the continuous adjoint equations for diffusion models, which we call AdjointDEIS. We exploit the unique construction of diffusion SDEs to further simplify the formulation of the continuous adjoint equations using exponential integrators. Moreover, we provide convergence order guarantees for our bespoke solvers. Significantly, we show that continuous adjoint equations for diffusion SDEs actually simplify to a simple ODE. Lastly, we demonstrate the effectiveness of AdjointDEIS for guided generation with an adversarial attack in the form of the face morphing problem. Our code will be released on our project page https://zblasingame.github.io/AdjointDEIS/

In this paper, we address the challenge of procedure planning in instructional videos, aiming to generate coherent and task-aligned action sequences from start and end visual observations. Previous work has mainly relied on text-level supervision to bridge the gap between observed states and unobserved actions, but it struggles with capturing intricate temporal relationships among actions. Building on these efforts, we propose the Masked Temporal Interpolation Diffusion (MTID) model that introduces a latent space temporal interpolation module within the diffusion model. This module leverages a learnable interpolation matrix to generate intermediate latent features, thereby augmenting visual supervision with richer mid-state details. By integrating this enriched supervision into the model, we enable end-to-end training tailored to task-specific requirements, significantly enhancing the model's capacity to predict temporally coherent action sequences. Additionally, we introduce an action-aware mask projection mechanism to restrict the action generation space, combined with a task-adaptive masked proximity loss to prioritize more accurate reasoning results close to the given start and end states over those in intermediate steps. Simultaneously, it filters out task-irrelevant action predictions, leading to contextually aware action sequences. Experimental results across three widely used benchmark datasets demonstrate that our MTID achieves promising action planning performance on most metrics. The code is available at https://github.com/WiserZhou/MTID.

Masked diffusion models (MDM) are powerful generative models for discrete data that generate samples by progressively unmasking tokens in a sequence. Each token can take one of two states: masked or unmasked. We observe that token sequences often remain unchanged between consecutive sampling steps; consequently, the model repeatedly processes identical inputs, leading to redundant computation. To address this inefficiency, we propose the Partial masking scheme (Prime), which augments MDM by allowing tokens to take intermediate states interpolated between the masked and unmasked states. This design enables the model to make predictions based on partially observed token information, and facilitates a fine-grained denoising process. We derive a variational training objective and introduce a simple architectural design to accommodate intermediate-state inputs. Our method demonstrates superior performance across a diverse set of generative modeling tasks. On text data, it achieves a perplexity of 15.36 on OpenWebText, outperforming previous MDM (21.52), autoregressive models (17.54), and their hybrid variants (17.58), without relying on an autoregressive formulation. On image data, it attains competitive FID scores of 3.26 on CIFAR-10 and 6.98 on ImageNet-32, comparable to leading continuous generative models.

Diffusion models are powerful generative models that allow for precise control over the characteristics of the generated samples. While these diffusion models trained on large datasets have achieved success, there is often a need to introduce additional controls in downstream fine-tuning processes, treating these powerful models as pre-trained diffusion models. This work presents a novel method based on reinforcement learning (RL) to add such controls using an offline dataset comprising inputs and labels. We formulate this task as an RL problem, with the classifier learned from the offline dataset and the KL divergence against pre-trained models serving as the reward functions. Our method, CTRL (Conditioning pre-Trained diffusion models with Reinforcement Learning), produces soft-optimal policies that maximize the abovementioned reward functions. We formally demonstrate that our method enables sampling from the conditional distribution with additional controls during inference. Our RL-based approach offers several advantages over existing methods. Compared to classifier-free guidance, it improves sample efficiency and can greatly simplify dataset construction by leveraging conditional independence between the inputs and additional controls. Additionally, unlike classifier guidance, it eliminates the need to train classifiers from intermediate states to additional controls. The code is available at https://github.com/zhaoyl18/CTRL.

Recent advances in diffusion transformers have shown remarkable generalization in visual synthesis, yet most dense perception methods still rely on text-to-image (T2I) generators designed for stochastic generation. We revisit this paradigm and show that image editing diffusion models are inherently image-to-image consistent, providing a more suitable foundation for dense perception task. We introduce Edit2Perceive, a unified diffusion framework that adapts editing models for depth, normal, and matting. Built upon the FLUX.1 Kontext architecture, our approach employs full-parameter fine-tuning and a pixel-space consistency loss to enforce structure-preserving refinement across intermediate denoising states. Moreover, our single-step deterministic inference yields up to faster runtime while training on relatively small datasets. Extensive experiments demonstrate comprehensive state-of-the-art results across all three tasks, revealing the strong potential of editing-oriented diffusion transformers for geometry-aware perception.

Diffusion models have emerged as powerful generative tools across various domains, yet tailoring pre-trained models to exhibit specific desirable properties remains challenging. While reinforcement learning (RL) offers a promising solution,current methods struggle to simultaneously achieve stable, efficient fine-tuning and support non-differentiable rewards. Furthermore, their reliance on sparse rewards provides inadequate supervision during intermediate steps, often resulting in suboptimal generation quality. To address these limitations, dense and differentiable signals are required throughout the diffusion process. Hence, we propose VAlue-based Reinforced Diffusion (VARD): a novel approach that first learns a value function predicting expection of rewards from intermediate states, and subsequently uses this value function with KL regularization to provide dense supervision throughout the generation process. Our method maintains proximity to the pretrained model while enabling effective and stable training via backpropagation. Experimental results demonstrate that our approach facilitates better trajectory guidance, improves training efficiency and extends the applicability of RL to diffusion models optimized for complex, non-differentiable reward functions.

Diffusion models excel at capturing the natural design spaces of images, molecules, DNA, RNA, and protein sequences. However, rather than merely generating designs that are natural, we often aim to optimize downstream reward functions while preserving the naturalness of these design spaces. Existing methods for achieving this goal often require ``differentiable'' proxy models (e.g., classifier guidance or DPS) or involve computationally expensive fine-tuning of diffusion models (e.g., classifier-free guidance, RL-based fine-tuning). In our work, we propose a new method to address these challenges. Our algorithm is an iterative sampling method that integrates soft value functions, which looks ahead to how intermediate noisy states lead to high rewards in the future, into the standard inference procedure of pre-trained diffusion models. Notably, our approach avoids fine-tuning generative models and eliminates the need to construct differentiable models. This enables us to (1) directly utilize non-differentiable features/reward feedback, commonly used in many scientific domains, and (2) apply our method to recent discrete diffusion models in a principled way. Finally, we demonstrate the effectiveness of our algorithm across several domains, including image generation, molecule generation, and DNA/RNA sequence generation. The code is available at https://github.com/masa-ue/SVDD{https://github.com/masa-ue/SVDD}.

Text-to-Image editing using diffusion models faces challenges in balancing content preservation with edit application and handling real-image editing. To address these, we propose LAMS-Edit, leveraging intermediate states from the inversion process--an essential step in real-image editing--during edited image generation. Specifically, latent representations and attention maps from both processes are combined at each step using weighted interpolation, controlled by a scheduler. This technique, Latent and Attention Mixing with Schedulers (LAMS), integrates with Prompt-to-Prompt (P2P) to form LAMS-Edit--an extensible framework that supports precise editing with region masks and enables style transfer via LoRA. Extensive experiments demonstrate that LAMS-Edit effectively balances content preservation and edit application.

Existing customization methods require access to multiple reference examples to align pre-trained diffusion probabilistic models (DPMs) with user-provided concepts. This paper aims to address the challenge of DPM customization when the only available supervision is a differentiable metric defined on the generated contents. Since the sampling procedure of DPMs involves recursive calls to the denoising UNet, na\"ive gradient backpropagation requires storing the intermediate states of all iterations, resulting in extremely high memory consumption. To overcome this issue, we propose a novel method AdjointDPM, which first generates new samples from diffusion models by solving the corresponding probability-flow ODEs. It then uses the adjoint sensitivity method to backpropagate the gradients of the loss to the models' parameters (including conditioning signals, network weights, and initial noises) by solving another augmented ODE. To reduce numerical errors in both the forward generation and gradient backpropagation processes, we further reparameterize the probability-flow ODE and augmented ODE as simple non-stiff ODEs using exponential integration. Finally, we demonstrate the effectiveness of AdjointDPM on three interesting tasks: converting visual effects into identification text embeddings, finetuning DPMs for specific types of stylization, and optimizing initial noise to generate adversarial samples for security auditing.

Though recent advances in multimodal models have demonstrated strong capabilities and opportunities in unified understanding and generation, the development of unified motion-language models remains underexplored. To enable such models with high-fidelity human motion, two core challenges must be addressed. The first is the reconstruction gap between the continuous motion modality and discrete representation in an autoregressive manner, and the second is the degradation of language intelligence during unified training. Inspired by the mixture of experts, we propose MotionGPT3, a bimodal motion-language model that treats human motion as a second modality, decoupling motion modeling via separate model parameters and enabling both effective cross-modal interaction and efficient multimodal scaling training. To preserve language intelligence, the text branch retains the original structure and parameters of the pretrained language model, while a new motion branch is integrated via a shared attention mechanism, enabling bidirectional information flow between two modalities. We first employ a motion Variational Autoencoder (VAE) to encode raw human motion into latent representations. Based on this continuous latent space, the motion branch predicts motion latents directly from intermediate hidden states using a diffusion head, bypassing discrete tokenization. Extensive experiments show that our approach achieves competitive performance on both motion understanding and generation tasks while preserving strong language capabilities, establishing a unified bimodal motion diffusion framework within an autoregressive manner.

Diffusion models, which can be viewed as a special case of hierarchical variational autoencoders (HVAEs), have shown profound success in generating photo-realistic images. In contrast, standard HVAEs often produce images of inferior quality compared to diffusion models. In this paper, we hypothesize that the success of diffusion models can be partly attributed to the additional self-supervision information for their intermediate latent states provided by corrupted images, which along with the original image form a pseudo video. Based on this hypothesis, we explore the possibility of improving other types of generative models with such pseudo videos. Specifically, we first extend a given image generative model to their video generative model counterpart, and then train the video generative model on pseudo videos constructed by applying data augmentation to the original images. Furthermore, we analyze the potential issues of first-order Markov data augmentation methods, which are typically used in diffusion models, and propose to use more expressive data augmentation to construct more useful information in pseudo videos. Our empirical results on the CIFAR10 and CelebA datasets demonstrate that improved image generation quality can be achieved with additional self-supervised information from pseudo videos.

3D Gaussian Splatting (3DGS) enhances 3D scene reconstruction through explicit representation and fast rendering, demonstrating potential benefits for various low-level vision tasks, including video compression. However, existing 3DGS-based video codecs generally exhibit more noticeable visual artifacts and relatively low compression ratios. In this paper, we specifically target the perceptual enhancement of 3DGS-based video compression, based on the assumption that artifacts from 3DGS rendering and quantization resemble noisy latents sampled during diffusion training. Building on this premise, we propose a content-adaptive framework, GFix, comprising a streamlined, single-step diffusion model that serves as an off-the-shelf neural enhancer. Moreover, to increase compression efficiency, We propose a modulated LoRA scheme that freezes the low-rank decompositions and modulates the intermediate hidden states, thereby achieving efficient adaptation of the diffusion backbone with highly compressible updates. Experimental results show that GFix delivers strong perceptual quality enhancement, outperforming GSVC with up to 72.1% BD-rate savings in LPIPS and 21.4% in FID.

Layout generation aims to synthesize realistic graphic scenes consisting of elements with different attributes including category, size, position, and between-element relation. It is a crucial task for reducing the burden on heavy-duty graphic design works for formatted scenes, e.g., publications, documents, and user interfaces (UIs). Diverse application scenarios impose a big challenge in unifying various layout generation subtasks, including conditional and unconditional generation. In this paper, we propose a Layout Diffusion Generative Model (LDGM) to achieve such unification with a single decoupled diffusion model. LDGM views a layout of arbitrary missing or coarse element attributes as an intermediate diffusion status from a completed layout. Since different attributes have their individual semantics and characteristics, we propose to decouple the diffusion processes for them to improve the diversity of training samples and learn the reverse process jointly to exploit global-scope contexts for facilitating generation. As a result, our LDGM can generate layouts either from scratch or conditional on arbitrary available attributes. Extensive qualitative and quantitative experiments demonstrate our proposed LDGM outperforms existing layout generation models in both functionality and performance.

Diffusion models have been widely used for conditional data cross-modal generation tasks such as text-to-image and text-to-video. However, state-of-the-art models still fail to align the generated visual concepts with high-level semantics in a language such as object count, spatial relationship, etc. We approach this problem from a multimodal data fusion perspective and investigate how different fusion strategies can affect vision-language alignment. We discover that compared to the widely used early fusion of conditioning text in a pretrained image feature space, a specially designed intermediate fusion can: (i) boost text-to-image alignment with improved generation quality and (ii) improve training and inference efficiency by reducing low-rank text-to-image attention calculations. We perform experiments using a text-to-image generation task on the MS-COCO dataset. We compare our intermediate fusion mechanism with the classic early fusion mechanism on two common conditioning methods on a U-shaped ViT backbone. Our intermediate fusion model achieves a higher CLIP Score and lower FID, with 20% reduced FLOPs, and 50% increased training speed compared to a strong U-ViT baseline with an early fusion.

Sequence modeling approaches have shown promising results in robot imitation learning. Recently, diffusion models have been adopted for behavioral cloning in a sequence modeling fashion, benefiting from their exceptional capabilities in modeling complex data distributions. The standard diffusion-based policy iteratively generates action sequences from random noise conditioned on the input states. Nonetheless, the model for diffusion policy can be further improved in terms of visual representations. In this work, we propose Crossway Diffusion, a simple yet effective method to enhance diffusion-based visuomotor policy learning via a carefully designed state decoder and an auxiliary self-supervised learning (SSL) objective. The state decoder reconstructs raw image pixels and other state information from the intermediate representations of the reverse diffusion process. The whole model is jointly optimized by the SSL objective and the original diffusion loss. Our experiments demonstrate the effectiveness of Crossway Diffusion in various simulated and real-world robot tasks, confirming its consistent advantages over the standard diffusion-based policy and substantial improvements over the baselines.

Conventional class-guided diffusion models generally succeed in generating images with correct semantic content, but often struggle with texture details. This limitation stems from the usage of class priors, which only provide coarse and limited conditional information. To address this issue, we propose Diffusion on Diffusion (DoD), an innovative multi-stage generation framework that first extracts visual priors from previously generated samples, then provides rich guidance for the diffusion model leveraging visual priors from the early stages of diffusion sampling. Specifically, we introduce a latent embedding module that employs a compression-reconstruction approach to discard redundant detail information from the conditional samples in each stage, retaining only the semantic information for guidance. We evaluate DoD on the popular ImageNet-256 times 256 dataset, reducing 7times training cost compared to SiT and DiT with even better performance in terms of the FID-50K score. Our largest model DoD-XL achieves an FID-50K score of 1.83 with only 1 million training steps, which surpasses other state-of-the-art methods without bells and whistles during inference.

Finding an initial noise vector that produces an input image when fed into the diffusion process (known as inversion) is an important problem in denoising diffusion models (DDMs), with applications for real image editing. The state-of-the-art approach for real image editing with inversion uses denoising diffusion implicit models (DDIMs) to deterministically noise the image to the intermediate state along the path that the denoising would follow given the original conditioning. However, DDIM inversion for real images is unstable as it relies on local linearization assumptions, which result in the propagation of errors, leading to incorrect image reconstruction and loss of content. To alleviate these problems, we propose Exact Diffusion Inversion via Coupled Transformations (EDICT), an inversion method that draws inspiration from affine coupling layers. EDICT enables mathematically exact inversion of real and model-generated images by maintaining two coupled noise vectors which are used to invert each other in an alternating fashion. Using Stable Diffusion, a state-of-the-art latent diffusion model, we demonstrate that EDICT successfully reconstructs real images with high fidelity. On complex image datasets like MS-COCO, EDICT reconstruction significantly outperforms DDIM, improving the mean square error of reconstruction by a factor of two. Using noise vectors inverted from real images, EDICT enables a wide range of image edits--from local and global semantic edits to image stylization--while maintaining fidelity to the original image structure. EDICT requires no model training/finetuning, prompt tuning, or extra data and can be combined with any pretrained DDM. Code is available at https://github.com/salesforce/EDICT.

This study presents a new image super-resolution (SR) technique based on diffusion inversion, aiming at harnessing the rich image priors encapsulated in large pre-trained diffusion models to improve SR performance. We design a Partial noise Prediction strategy to construct an intermediate state of the diffusion model, which serves as the starting sampling point. Central to our approach is a deep noise predictor to estimate the optimal noise maps for the forward diffusion process. Once trained, this noise predictor can be used to initialize the sampling process partially along the diffusion trajectory, generating the desirable high-resolution result. Compared to existing approaches, our method offers a flexible and efficient sampling mechanism that supports an arbitrary number of sampling steps, ranging from one to five. Even with a single sampling step, our method demonstrates superior or comparable performance to recent state-of-the-art approaches. The code and model are publicly available at https://github.com/zsyOAOA/InvSR.

Diffusion models are the current state-of-the-art in image generation, synthesizing high-quality images by breaking down the generation process into many fine-grained denoising steps. Despite their good performance, diffusion models are computationally expensive, requiring many neural function evaluations (NFEs). In this work, we propose an anytime diffusion-based method that can generate viable images when stopped at arbitrary times before completion. Using existing pretrained diffusion models, we show that the generation scheme can be recomposed as two nested diffusion processes, enabling fast iterative refinement of a generated image. We use this Nested Diffusion approach to peek into the generation process and enable flexible scheduling based on the instantaneous preference of the user. In experiments on ImageNet and Stable Diffusion-based text-to-image generation, we show, both qualitatively and quantitatively, that our method's intermediate generation quality greatly exceeds that of the original diffusion model, while the final slow generation result remains comparable.

Flow-based generative models have shown remarkable success in text-to-image generation, yet fine-tuning them with intermediate feedback remains challenging, especially for continuous-time flow matching models. Most existing approaches solely learn from outcome rewards, struggling with the credit assignment problem. Alternative methods that attempt to learn a critic via direct regression on cumulative rewards often face training instabilities and model collapse in online settings. We present AC-Flow, a robust actor-critic framework that addresses these challenges through three key innovations: (1) reward shaping that provides well-normalized learning signals to enable stable intermediate value learning and gradient control, (2) a novel dual-stability mechanism that combines advantage clipping to prevent destructive policy updates with a warm-up phase that allows the critic to mature before influencing the actor, and (3) a scalable generalized critic weighting scheme that extends traditional reward-weighted methods while preserving model diversity through Wasserstein regularization. Through extensive experiments on Stable Diffusion 3, we demonstrate that AC-Flow achieves state-of-the-art performance in text-to-image alignment tasks and generalization to unseen human preference models. Our results demonstrate that even with a computationally efficient critic model, we can robustly finetune flow models without compromising generative quality, diversity, or stability.

Diffusion model-based inverse problem solvers have demonstrated state-of-the-art performance in cases where the forward operator is known (i.e. non-blind). However, the applicability of the method to blind inverse problems has yet to be explored. In this work, we show that we can indeed solve a family of blind inverse problems by constructing another diffusion prior for the forward operator. Specifically, parallel reverse diffusion guided by gradients from the intermediate stages enables joint optimization of both the forward operator parameters as well as the image, such that both are jointly estimated at the end of the parallel reverse diffusion procedure. We show the efficacy of our method on two representative tasks -- blind deblurring, and imaging through turbulence -- and show that our method yields state-of-the-art performance, while also being flexible to be applicable to general blind inverse problems when we know the functional forms.

Mesh models have become increasingly accessible for numerous cities; however, the lack of realistic textures restricts their application in virtual urban navigation and autonomous driving. To address this, this paper proposes MeSS (Meshbased Scene Synthesis) for generating high-quality, styleconsistent outdoor scenes with city mesh models serving as the geometric prior. While image and video diffusion models can leverage spatial layouts (such as depth maps or HD maps) as control conditions to generate street-level perspective views, they are not directly applicable to 3D scene generation. Video diffusion models excel at synthesizing consistent view sequences that depict scenes but often struggle to adhere to predefined camera paths or align accurately with rendered control videos. In contrast, image diffusion models, though unable to guarantee cross-view visual consistency, can produce more geometry-aligned results when combined with ControlNet. Building on this insight, our approach enhances image diffusion models by improving cross-view consistency. The pipeline comprises three key stages: first, we generate geometrically consistent sparse views using Cascaded Outpainting ControlNets; second, we propagate denser intermediate views via a component dubbed AGInpaint; and third, we globally eliminate visual inconsistencies (e.g., varying exposure) using the GCAlign module. Concurrently with generation, a 3D Gaussian Splatting (3DGS) scene is reconstructed by initializing Gaussian balls on the mesh surface. Our method outperforms existing approaches in both geometric alignment and generation quality. Once synthesized, the scene can be rendered in diverse styles through relighting and style transfer techniques.

Fast and high-quality language generation is the holy grail that people pursue in the age of AI. In this work, we introduce Discrete Diffusion Divergence Instruct (DiDi-Instruct), a training-based method that initializes from a pre-trained (masked) discrete diffusion language model (dLLM) and distills a few-step student for fast generation. The resulting DiDi-Instruct model achieves comparable or superior performance to its dLLM teacher and the GPT-2 baseline while enabling up to 64times acceleration. The theoretical foundation of DiDi-Instruct is a novel framework based on integral KL-divergence minimization, which yields a practical training algorithm. We further introduce grouped reward normalization, intermediate-state matching, and the reward-guided ancestral sampler that significantly improve training stability, model coverage, and inference quality. On OpenWebText, DiDi-Instruct achieves perplexity from 62.2 (8 NFEs) to 18.4 (128 NFEs), which outperforms prior accelerated dLLMs and GPT-2 baseline. These gains come with a negligible entropy loss (around 1%) and reduce additional training wall-clock time by more than 20times compared to competing dLLM distillation methods. We further validate the robustness and effectiveness of DiDi-Instruct through extensive ablation studies, model scaling, and the generation of discrete protein sequences. In conclusion, DiDi-Instruct is an efficient yet effective distillation method, enabling language generation in the blink of an eye. We will release both code and models at github.com/haoyangzheng-ai/didi-instruct.

Diffusion Transformers (DiTs) have demonstrated remarkable generative capabilities, particularly benefiting from Transformer architectures that enhance visual and artistic fidelity. However, their inherently sequential denoising process results in high inference latency, limiting their deployment in real-time scenarios. Existing training-free acceleration approaches typically reuse intermediate features at fixed timesteps or layers, overlooking the evolving semantic focus across denoising stages and Transformer blocks.To address this, we propose Sortblock, a training-free inference acceleration framework that dynamically caches block-wise features based on their similarity across adjacent timesteps. By ranking the evolution of residuals, Sortblock adaptively determines a recomputation ratio, selectively skipping redundant computations while preserving generation quality. Furthermore, we incorporate a lightweight linear prediction mechanism to reduce accumulated errors in skipped blocks.Extensive experiments across various tasks and DiT architectures demonstrate that Sortblock achieves over 2times inference speedup with minimal degradation in output quality, offering an effective and generalizable solution for accelerating diffusion-based generative models.

Diffusion models have demonstrated remarkable capabilities in visual content generation but remain challenging to deploy due to their high computational cost during inference. This computational burden primarily arises from the quadratic complexity of self-attention with respect to image or video resolution. While existing acceleration methods often compromise output quality or necessitate costly retraining, we observe that most diffusion models are pre-trained at lower resolutions, presenting an opportunity to exploit these low-resolution priors for more efficient inference without degrading performance. In this work, we introduce Bottleneck Sampling, a training-free framework that leverages low-resolution priors to reduce computational overhead while preserving output fidelity. Bottleneck Sampling follows a high-low-high denoising workflow: it performs high-resolution denoising in the initial and final stages while operating at lower resolutions in intermediate steps. To mitigate aliasing and blurring artifacts, we further refine the resolution transition points and adaptively shift the denoising timesteps at each stage. We evaluate Bottleneck Sampling on both image and video generation tasks, where extensive experiments demonstrate that it accelerates inference by up to 3times for image generation and 2.5times for video generation, all while maintaining output quality comparable to the standard full-resolution sampling process across multiple evaluation metrics. Code is available at: https://github.com/tyfeld/Bottleneck-Sampling

While recent Flow Matching models avoid the reconstruction bottlenecks of latent autoencoders by operating directly in pixel space, the lack of semantic continuity in the pixel manifold severely intertwines optimal transport paths. This induces severe trajectory conflicts near intersections, yielding sub-optimal solutions. Rather than bypassing this issue via information-lossy latent representations, we directly untangle the pixel-space trajectories by proposing Waypoint Diffusion Transformers (WiT). WiT factorizes the continuous vector field via intermediate semantic waypoints projected from pre-trained vision models. It effectively disentangles the generation trajectories by breaking the optimal transport into prior-to-waypoint and waypoint-to-pixel segments. Specifically, during the iterative denoising process, a lightweight generator dynamically infers these intermediate waypoints from the current noisy state. They then continuously condition the primary diffusion transformer via the Just-Pixel AdaLN mechanism, steering the evolution towards the next state, ultimately yielding the final RGB pixels. Evaluated on ImageNet 256x256, WiT beats strong pixel-space baselines, accelerating JiT training convergence by 2.2x. Code will be publicly released at https://github.com/hainuo-wang/WiT.git.

Building state-of-the-art Vision-Language Models (VLMs) with strong captioning capabilities typically necessitates training on billions of high-quality image-text pairs, requiring millions of GPU hours. This paper introduces the Vision-Language-Vision (VLV) auto-encoder framework, which strategically leverages key pretrained components: a vision encoder, the decoder of a Text-to-Image (T2I) diffusion model, and subsequently, a Large Language Model (LLM). Specifically, we establish an information bottleneck by regularizing the language representation space, achieved through freezing the pretrained T2I diffusion decoder. Our VLV pipeline effectively distills knowledge from the text-conditioned diffusion model using continuous embeddings, demonstrating comprehensive semantic understanding via high-quality reconstructions. Furthermore, by fine-tuning a pretrained LLM to decode the intermediate language representations into detailed descriptions, we construct a state-of-the-art (SoTA) captioner comparable to leading models like GPT-4o and Gemini 2.0 Flash. Our method demonstrates exceptional cost-efficiency and significantly reduces data requirements; by primarily utilizing single-modal images for training and maximizing the utility of existing pretrained models (image encoder, T2I diffusion model, and LLM), it circumvents the need for massive paired image-text datasets, keeping the total training expenditure under $1,000 USD.

While deep learning-based methods for blind face restoration have achieved unprecedented success, they still suffer from two major limitations. First, most of them deteriorate when facing complex degradations out of their training data. Second, these methods require multiple constraints, e.g., fidelity, perceptual, and adversarial losses, which require laborious hyper-parameter tuning to stabilize and balance their influences. In this work, we propose a novel method named DifFace that is capable of coping with unseen and complex degradations more gracefully without complicated loss designs. The key of our method is to establish a posterior distribution from the observed low-quality (LQ) image to its high-quality (HQ) counterpart. In particular, we design a transition distribution from the LQ image to the intermediate state of a pre-trained diffusion model and then gradually transmit from this intermediate state to the HQ target by recursively applying a pre-trained diffusion model. The transition distribution only relies on a restoration backbone that is trained with L_2 loss on some synthetic data, which favorably avoids the cumbersome training process in existing methods. Moreover, the transition distribution can contract the error of the restoration backbone and thus makes our method more robust to unknown degradations. Comprehensive experiments show that DifFace is superior to current state-of-the-art methods, especially in cases with severe degradations. Our code and model are available at https://github.com/zsyOAOA/DifFace.

Sepsis remains one of the leading causes of mortality in intensive care units, where timely and accurate treatment decisions can significantly impact patient outcomes. In this work, we propose an interpretable decision support framework. Our system integrates four core components: (1) a clustering-based stratification module that categorizes patients into low, intermediate, and high-risk groups upon ICU admission, using clustering with statistical validation; (2) a synthetic data augmentation pipeline leveraging variational autoencoders (VAE) and diffusion models to enrich underrepresented trajectories such as fluid or vasopressor administration; (3) an offline reinforcement learning (RL) agent trained using Advantage Weighted Regression (AWR) with a lightweight attention encoder and supported by an ensemble models for conservative, safety-aware treatment recommendations; and (4) a rationale generation module powered by a multi-modal large language model (LLM), which produces natural-language justifications grounded in clinical context and retrieved expert knowledge. Evaluated on the MIMIC-III and eICU datasets, our approach achieves high treatment accuracy while providing clinicians with interpretable and robust policy recommendations.

We introduce Interleaved Gibbs Diffusion (IGD), a novel generative modeling framework for mixed continuous-discrete data, focusing on constrained generation problems. Prior works on discrete and continuous-discrete diffusion models assume factorized denoising distribution for fast generation, which can hinder the modeling of strong dependencies between random variables encountered in constrained generation. IGD moves beyond this by interleaving continuous and discrete denoising algorithms via a discrete time Gibbs sampling type Markov chain. IGD provides flexibility in the choice of denoisers, allows conditional generation via state-space doubling and inference time scaling via the ReDeNoise method. Empirical evaluations on three challenging tasks-solving 3-SAT, generating molecule structures, and generating layouts-demonstrate state-of-the-art performance. Notably, IGD achieves a 7% improvement on 3-SAT out of the box and achieves state-of-the-art results in molecule generation without relying on equivariant diffusion or domain-specific architectures. We explore a wide range of modeling, and interleaving strategies along with hyperparameters in each of these problems.

In recent years, diffusion-based models have demonstrated exceptional performance in searching for simultaneously stable, unique, and novel (S.U.N.) crystalline materials. However, most of these models don't have the ability to change the number of atoms in the crystal during the generation process, which limits the variability of model sampling trajectories. In this paper, we demonstrate the severity of this restriction and introduce a simple yet powerful technique, mirage infusion, which enables diffusion models to change the state of the atoms that make up the crystal from existent to non-existent (mirage) and vice versa. We show that this technique improves model quality by up to times2.5 compared to the same model without this modification. The resulting model, Mirage Atom Diffusion (MiAD), is an equivariant joint diffusion model for de novo crystal generation that is capable of altering the number of atoms during the generation process. MiAD achieves an 8.2% S.U.N. rate on the MP-20 dataset, which substantially exceeds existing state-of-the-art approaches. The source code can be found at https://github.com/andrey-okhotin/miad.git{github.com/andrey-okhotin/miad}.

The final state interactions (FSI) model in which soft rescattering of low mass intermediate states dominates is suggested. It explains why the strong interaction phases are large in the B_dtopipi channel and are considerably smaller in the B_dtorhorho one. Direct CP asymmetries of B_dtopipi decays which are determined by FSI phases are considered as well.

In this paper, we point out suboptimal noise-data mapping leads to slow training of diffusion models. During diffusion training, current methods diffuse each image across the entire noise space, resulting in a mixture of all images at every point in the noise layer. We emphasize that this random mixture of noise-data mapping complicates the optimization of the denoising function in diffusion models. Drawing inspiration from the immiscible phenomenon in physics, we propose Immiscible Diffusion, a simple and effective method to improve the random mixture of noise-data mapping. In physics, miscibility can vary according to various intermolecular forces. Thus, immiscibility means that the mixing of the molecular sources is distinguishable. Inspired by this, we propose an assignment-then-diffusion training strategy. Specifically, prior to diffusing the image data into noise, we assign diffusion target noise for the image data by minimizing the total image-noise pair distance in a mini-batch. The assignment functions analogously to external forces to separate the diffuse-able areas of images, thus mitigating the inherent difficulties in diffusion training. Our approach is remarkably simple, requiring only one line of code to restrict the diffuse-able area for each image while preserving the Gaussian distribution of noise. This ensures that each image is projected only to nearby noise. To address the high complexity of the assignment algorithm, we employ a quantized-assignment method to reduce the computational overhead to a negligible level. Experiments demonstrate that our method achieve up to 3x faster training for consistency models and DDIM on the CIFAR dataset, and up to 1.3x faster on CelebA datasets for consistency models. Besides, we conduct thorough analysis about the Immiscible Diffusion, which sheds lights on how it improves diffusion training speed while improving the fidelity.

We introduce MoS (Mixture of States), a novel fusion paradigm for multimodal diffusion models that merges modalities using flexible, state-based interactions. The core of MoS is a learnable, token-wise router that creates denoising timestep- and input-dependent interactions between modalities' hidden states, precisely aligning token-level features with the diffusion trajectory. This router sparsely selects the top-k hidden states and is trained with an ε-greedy strategy, efficiently selecting contextual features with minimal learnable parameters and negligible computational overhead. We validate our design with text-to-image generation (MoS-Image) and editing (MoS-Editing), which achieve state-of-the-art results. With only 3B to 5B parameters, our models match or surpass counterparts up to 4times larger. These findings establish MoS as a flexible and compute-efficient paradigm for scaling multimodal diffusion models.

We propose a quantum version of a generative diffusion model. In this algorithm, artificial neural networks are replaced with parameterized quantum circuits, in order to directly generate quantum states. We present both a full quantum and a latent quantum version of the algorithm; we also present a conditioned version of these models. The models' performances have been evaluated using quantitative metrics complemented by qualitative assessments. An implementation of a simplified version of the algorithm has been executed on real NISQ quantum hardware.

We investigate the time evolution of the Boltzmann entropy of a dilute gas of N particles, N>>1, as it undergoes a free expansion doubling its volume. The microstate of the system, a point in the 4N dimensional phase space, changes in time via Hamiltonian dynamics. Its entropy, at any time t, is given by the logarithm of the phase space volume of all the microstates giving rise to its macrostate at time t. The macrostates that we consider are defined by coarse graining the one-particle phase space into cells Δ_α. The initial and final macrostates of the system are equilibrium states in volumes V and 2V, with the same energy E and particle number N. Their entropy per particle is given, for sufficiently large systems, by the thermodynamic entropy as a function of the particle and energy density, whose leading term is independent of the size of the Δ_α. The intermediate (non-equilibrium) entropy does however depend on the size of the cells Δ_α. Its change with time is due to (i) dispersal in physical space from free motion and to (ii) the collisions between particles which change their velocities. The former depends strongly on the size of the velocity coarse graining Δv: it produces entropy at a rate proportional to Δv. This dependence is investigated numerically and analytically for a dilute two-dimensional gas of hard discs. It becomes significant when the mean free path between collisions is of the same order or larger than the length scale of the initial spatial inhomogeneity. In the opposite limit, the rate of entropy production is essentially independent of Δv and is given by the Boltzmann equation for the limit Δvrightarrow 0. We show that when both processes are active the time dependence of the entropy has a scaling form involving the ratio of the rates of its production by the two processes.

How do diffusion generative models convert pure noise into meaningful images? In a variety of pretrained diffusion models (including conditional latent space models like Stable Diffusion), we observe that the reverse diffusion process that underlies image generation has the following properties: (i) individual trajectories tend to be low-dimensional and resemble 2D `rotations'; (ii) high-variance scene features like layout tend to emerge earlier, while low-variance details tend to emerge later; and (iii) early perturbations tend to have a greater impact on image content than later perturbations. To understand these phenomena, we derive and study a closed-form solution to the probability flow ODE for a Gaussian distribution, which shows that the reverse diffusion state rotates towards a gradually-specified target on the image manifold. It also shows that generation involves first committing to an outline, and then to finer and finer details. We find that this solution accurately describes the initial phase of image generation for pretrained models, and can in principle be used to make image generation more efficient by skipping reverse diffusion steps. Finally, we use our solution to characterize the image manifold in Stable Diffusion. Our viewpoint reveals an unexpected similarity between generation by GANs and diffusion and provides a conceptual link between diffusion and image retrieval.

The interdiffusion coefficients are estimated either following the Wagner's method expressed with respect to the composition (mol or atomic fraction) normalized variable after considering the molar volume variation or the den Broeder's method expressed with respect to the concentration (composition divided by the molar volume) normalized variable. On the other hand, the relations for estimation of the intrinsic diffusion coefficients of components as established by van Loo and integrated diffusion coefficients in a phase with narrow homogeneity range as established by Wagner are currently available with respect to the composition normalized variable only. In this study, we have first derived the relation proposed by den Broeder following the line of treatment proposed by Wagner. Further, the relations for estimation of the intrinsic diffusion coefficients of the components and integrated interdiffusion coefficient are established with respect to the concentration normalized variable, which were not available earlier. The veracity of these methods is examined based on the estimation of data in Ni-Pd, Ni-Al and Cu-Sn systems. Our analysis indicates that both the approaches are logically correct and there is small difference in the estimated data in these systems although a higher difference could be found in other systems. The integrated interdiffusion coefficients with respect to the concentration (or concentration normalized variable) can only be estimated considering the ideal molar volume variation. This might be drawback in certain practical systems.

We study in detail a one-dimensional lattice model of a continuum, conserved field (mass) that is transferred deterministically between neighbouring random sites. The model falls in a wider class of lattice models capturing the joint effect of random advection and diffusion and encompassing as specific cases, some models studied in the literature, like the Kang-Redner, Kipnis-Marchioro-Presutti, Takayasu-Taguchi, etc. The motivation for our setup comes from a straightforward interpretation as advection of particles in one-dimensional turbulence, but it is also related to a problem of synchronization of dynamical systems driven by common noise. For finite lattices, we study both the coalescence of an initially spread field (interpreted as roughening), and the statistical steady-state properties. We distinguish two main size-dependent regimes, depending on the strength of the diffusion term and on the lattice size. Using numerical simulations and mean-field approach, we study the statistics of the field. For weak diffusion, we unveil a characteristic hierarchical structure of the field. We also connect the model and the iterated function systems concept.

Colloquially speaking, image generation models based upon diffusion processes are frequently said to exhibit "hallucinations," samples that could never occur in the training data. But where do such hallucinations come from? In this paper, we study a particular failure mode in diffusion models, which we term mode interpolation. Specifically, we find that diffusion models smoothly "interpolate" between nearby data modes in the training set, to generate samples that are completely outside the support of the original training distribution; this phenomenon leads diffusion models to generate artifacts that never existed in real data (i.e., hallucinations). We systematically study the reasons for, and the manifestation of this phenomenon. Through experiments on 1D and 2D Gaussians, we show how a discontinuous loss landscape in the diffusion model's decoder leads to a region where any smooth approximation will cause such hallucinations. Through experiments on artificial datasets with various shapes, we show how hallucination leads to the generation of combinations of shapes that never existed. Finally, we show that diffusion models in fact know when they go out of support and hallucinate. This is captured by the high variance in the trajectory of the generated sample towards the final few backward sampling process. Using a simple metric to capture this variance, we can remove over 95% of hallucinations at generation time while retaining 96% of in-support samples. We conclude our exploration by showing the implications of such hallucination (and its removal) on the collapse (and stabilization) of recursive training on synthetic data with experiments on MNIST and 2D Gaussians dataset. We release our code at https://github.com/locuslab/diffusion-model-hallucination.

Diffusion models are the standard toolkit for generative modelling of 3D atomic systems. However, for different types of atomic systems - such as molecules and materials - the generative processes are usually highly specific to the target system despite the underlying physics being the same. We introduce the All-atom Diffusion Transformer (ADiT), a unified latent diffusion framework for jointly generating both periodic materials and non-periodic molecular systems using the same model: (1) An autoencoder maps a unified, all-atom representations of molecules and materials to a shared latent embedding space; and (2) A diffusion model is trained to generate new latent embeddings that the autoencoder can decode to sample new molecules or materials. Experiments on QM9 and MP20 datasets demonstrate that jointly trained ADiT generates realistic and valid molecules as well as materials, exceeding state-of-the-art results from molecule and crystal-specific models. ADiT uses standard Transformers for both the autoencoder and diffusion model, resulting in significant speedups during training and inference compared to equivariant diffusion models. Scaling ADiT up to half a billion parameters predictably improves performance, representing a step towards broadly generalizable foundation models for generative chemistry. Open source code: https://github.com/facebookresearch/all-atom-diffusion-transformer

A class of generative models that unifies flow-based and diffusion-based methods is introduced. These models extend the framework proposed in Albergo & Vanden-Eijnden (2023), enabling the use of a broad class of continuous-time stochastic processes called `stochastic interpolants' to bridge any two arbitrary probability density functions exactly in finite time. These interpolants are built by combining data from the two prescribed densities with an additional latent variable that shapes the bridge in a flexible way. The time-dependent probability density function of the stochastic interpolant is shown to satisfy a first-order transport equation as well as a family of forward and backward Fokker-Planck equations with tunable diffusion coefficient. Upon consideration of the time evolution of an individual sample, this viewpoint immediately leads to both deterministic and stochastic generative models based on probability flow equations or stochastic differential equations with an adjustable level of noise. The drift coefficients entering these models are time-dependent velocity fields characterized as the unique minimizers of simple quadratic objective functions, one of which is a new objective for the score of the interpolant density. We show that minimization of these quadratic objectives leads to control of the likelihood for generative models built upon stochastic dynamics, while likelihood control for deterministic dynamics is more stringent. We also discuss connections with other methods such as score-based diffusion models, stochastic localization processes, probabilistic denoising techniques, and rectifying flows. In addition, we demonstrate that stochastic interpolants recover the Schr\"odinger bridge between the two target densities when explicitly optimizing over the interpolant. Finally, algorithmic aspects are discussed and the approach is illustrated on numerical examples.

Temporal causal representation learning methods assume that causal mechanisms switch instantaneously between discrete domains, yet real-world systems often exhibit continuous mechanism transitions. For example, a vehicle's dynamics evolve gradually through a turning maneuver, and human gait shifts smoothly from walking to running. We formalize this setting by modeling transitional mechanisms as convex combinations of finitely many atomic mechanisms, governed by time-varying mixing coefficients. Our theoretical contributions establish that both the latent causal variables and the continuous mixing trajectory are jointly identifiable. We further propose TRACE, a Mixture-of-Experts framework where each expert learns one atomic mechanism during training, enabling recovery of mechanism trajectories at test time. This formulation generalizes to intermediate mechanism states never observed during training. Experiments on synthetic and real-world data demonstrate that TRACE recovers mixing trajectories with up to 0.99 correlation, substantially outperforming discrete-switching baselines.

Diffusion models have gained prominence in generating high-quality sequences of text. Nevertheless, current approaches predominantly represent discrete text within a continuous diffusion space, which incurs substantial computational overhead during training and results in slower sampling speeds. In this paper, we introduce a soft absorbing state that facilitates the diffusion model in learning to reconstruct discrete mutations based on the underlying Gaussian space, thereby enhancing its capacity to recover conditional signals. During the sampling phase, we employ state-of-the-art ODE solvers within the continuous space to expedite the sampling process. Comprehensive experimental evaluations reveal that our proposed method effectively accelerates the training convergence by 4x and generates samples of similar quality 800x faster, rendering it significantly closer to practical application. The code is released at \url{https://github.com/Shark-NLP/DiffuSeq

The friction coefficient of a particle can depend on its position as it does when the particle is near a wall. We formulate the dynamics of particles with such state-dependent friction coefficients in terms of a general Langevin equation with multiplicative noise, whose evaluation requires the introduction of specific rules. Two common conventions, the Ito and the Stratonovich, provide alternative rules for evaluation of the noise, but other conventions are possible. We show the requirement that a particle's distribution function approach the Boltzmann distribution at long times dictates that a drift term must be added to the Langevin equation. This drift term is proportional to the derivative of the diffusion coefficient times a factor that depends on the convention used to define the multiplicative noise. We explore the consequences of this result in a number examples with spatially varying diffusion coefficients. We also derive path integral representations for arbitrary interpretation of the noise, and use it in a perturbative study of correlations in a simple system.

Flow map models such as Consistency Models (CM) and Mean Flow (MF) enable few-step generation by learning the long jump of the ODE solution of diffusion models, yet training remains unstable, sensitive to hyperparameters, and costly. Initializing from a pre-trained diffusion model helps, but still requires converting infinitesimal steps into a long-jump map, leaving instability unresolved. We introduce mid-training, the first concept and practical method that inserts a lightweight intermediate stage between the (diffusion) pre-training and the final flow map training (i.e., post-training) for vision generation. Concretely, Consistency Mid-Training (CMT) is a compact and principled stage that trains a model to map points along a solver trajectory from a pre-trained model, starting from a prior sample, directly to the solver-generated clean sample. It yields a trajectory-consistent and stable initialization. This initializer outperforms random and diffusion-based baselines and enables fast, robust convergence without heuristics. Initializing post-training with CMT weights further simplifies flow map learning. Empirically, CMT achieves state of the art two step FIDs: 1.97 on CIFAR-10, 1.32 on ImageNet 64x64, and 1.84 on ImageNet 512x512, while using up to 98% less training data and GPU time, compared to CMs. On ImageNet 256x256, CMT reaches 1-step FID 3.34 while cutting total training time by about 50% compared to MF from scratch (FID 3.43). This establishes CMT as a principled, efficient, and general framework for training flow map models.

This paper introduces the Quantum Generative Diffusion Model (QGDM), a fully quantum-mechanical model for generating quantum state ensembles, inspired by Denoising Diffusion Probabilistic Models. QGDM features a diffusion process that introduces timestep-dependent noise into quantum states, paired with a denoising mechanism trained to reverse this contamination. This model efficiently evolves a completely mixed state into a target quantum state post-training. Our comparative analysis with Quantum Generative Adversarial Networks demonstrates QGDM's superiority, with fidelity metrics exceeding 0.99 in numerical simulations involving up to 4 qubits. Additionally, we present a Resource-Efficient version of QGDM (RE-QGDM), which minimizes the need for auxiliary qubits while maintaining impressive generative capabilities for tasks involving up to 8 qubits. These results showcase the proposed models' potential for tackling challenging quantum generation problems.

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.

Despite the remarkable success of diffusion models in image generation, slow sampling remains a persistent issue. To accelerate the sampling process, prior studies have reformulated diffusion sampling as an ODE/SDE and introduced higher-order numerical methods. However, these methods often produce divergence artifacts, especially with a low number of sampling steps, which limits the achievable acceleration. In this paper, we investigate the potential causes of these artifacts and suggest that the small stability regions of these methods could be the principal cause. To address this issue, we propose two novel techniques. The first technique involves the incorporation of Heavy Ball (HB) momentum, a well-known technique for improving optimization, into existing diffusion numerical methods to expand their stability regions. We also prove that the resulting methods have first-order convergence. The second technique, called Generalized Heavy Ball (GHVB), constructs a new high-order method that offers a variable trade-off between accuracy and artifact suppression. Experimental results show that our techniques are highly effective in reducing artifacts and improving image quality, surpassing state-of-the-art diffusion solvers on both pixel-based and latent-based diffusion models for low-step sampling. Our research provides novel insights into the design of numerical methods for future diffusion work.

Recently, various methods have been proposed to address the inconsistency issue of DDIM inversion to enable image editing, such as EDICT [36] and Null-text inversion [22]. However, the above methods introduce considerable computational overhead. In this paper, we propose a new technique, named bi-directional integration approximation (BDIA), to perform exact diffusion inversion with neglible computational overhead. Suppose we would like to estimate the next diffusion state z_{i-1} at timestep t_i with the historical information (i,z_i) and (i+1,z_{i+1}). We first obtain the estimated Gaussian noise boldsymbol{epsilon}(z_i,i), and then apply the DDIM update procedure twice for approximating the ODE integration over the next time-slot [t_i, t_{i-1}] in the forward manner and the previous time-slot [t_i, t_{t+1}] in the backward manner. The DDIM step for the previous time-slot is used to refine the integration approximation made earlier when computing z_i. A nice property of BDIA-DDIM is that the update expression for z_{i-1} is a linear combination of (z_{i+1}, z_i, boldsymbol{epsilon}(z_i,i)). This allows for exact backward computation of z_{i+1} given (z_i, z_{i-1}), thus leading to exact diffusion inversion. It is demonstrated with experiments that (round-trip) BDIA-DDIM is particularly effective for image editing. Our experiments further show that BDIA-DDIM produces markedly better image sampling qualities than DDIM for text-to-image generation. BDIA can also be applied to improve the performance of other ODE solvers in addition to DDIM. In our work, it is found that applying BDIA to the EDM sampling procedure produces consistently better performance over four pre-trained models.

A fundamental dilemma in generative modeling persists: iterative diffusion models achieve outstanding fidelity, but at a significant computational cost, while efficient few-step alternatives are constrained by a hard quality ceiling. This conflict between generation steps and output quality arises from restrictive training objectives that focus exclusively on either infinitesimal dynamics (PF-ODEs) or direct endpoint prediction. We address this challenge by introducing an exact, continuous-time dynamics equation that analytically defines state transitions across any finite time interval. This leads to a novel generative paradigm, Transition Models (TiM), which adapt to arbitrary-step transitions, seamlessly traversing the generative trajectory from single leaps to fine-grained refinement with more steps. Despite having only 865M parameters, TiM achieves state-of-the-art performance, surpassing leading models such as SD3.5 (8B parameters) and FLUX.1 (12B parameters) across all evaluated step counts. Importantly, unlike previous few-step generators, TiM demonstrates monotonic quality improvement as the sampling budget increases. Additionally, when employing our native-resolution strategy, TiM delivers exceptional fidelity at resolutions up to 4096x4096.

Diffusion models degrade images through noise, and reversing this process reveals an information hierarchy across timesteps. Scale-space theory exhibits a similar hierarchy via low-pass filtering. We formalize this connection and show that highly noisy diffusion states contain no more information than small, downsampled images - raising the question of why they must be processed at full resolution. To address this, we fuse scale spaces into the diffusion process by formulating a family of diffusion models with generalized linear degradations and practical implementations. Using downsampling as the degradation yields our proposed Scale Space Diffusion. To support Scale Space Diffusion, we introduce Flexi-UNet, a UNet variant that performs resolution-preserving and resolution-increasing denoising using only the necessary parts of the network. We evaluate our framework on CelebA and ImageNet and analyze its scaling behavior across resolutions and network depths. Our project website ( https://prateksha.github.io/projects/scale-space-diffusion/ ) is available publicly.

While deep neural networks (NN) significantly advance image compressed sensing (CS) by improving reconstruction quality, the necessity of training current CS NNs from scratch constrains their effectiveness and hampers rapid deployment. Although recent methods utilize pre-trained diffusion models for image reconstruction, they struggle with slow inference and restricted adaptability to CS. To tackle these challenges, this paper proposes Invertible Diffusion Models (IDM), a novel efficient, end-to-end diffusion-based CS method. IDM repurposes a large-scale diffusion sampling process as a reconstruction model, and fine-tunes it end-to-end to recover original images directly from CS measurements, moving beyond the traditional paradigm of one-step noise estimation learning. To enable such memory-intensive end-to-end fine-tuning, we propose a novel two-level invertible design to transform both (1) multi-step sampling process and (2) noise estimation U-Net in each step into invertible networks. As a result, most intermediate features are cleared during training to reduce up to 93.8% GPU memory. In addition, we develop a set of lightweight modules to inject measurements into noise estimator to further facilitate reconstruction. Experiments demonstrate that IDM outperforms existing state-of-the-art CS networks by up to 2.64dB in PSNR. Compared to the recent diffusion-based approach DDNM, our IDM achieves up to 10.09dB PSNR gain and 14.54 times faster inference. Code is available at https://github.com/Guaishou74851/IDM.

Riemannian diffusion models draw inspiration from standard Euclidean space diffusion models to learn distributions on general manifolds. Unfortunately, the additional geometric complexity renders the diffusion transition term inexpressible in closed form, so prior methods resort to imprecise approximations of the score matching training objective that degrade performance and preclude applications in high dimensions. In this work, we reexamine these approximations and propose several practical improvements. Our key observation is that most relevant manifolds are symmetric spaces, which are much more amenable to computation. By leveraging and combining various ans\"{a}tze, we can quickly compute relevant quantities to high precision. On low dimensional datasets, our correction produces a noticeable improvement, allowing diffusion to compete with other methods. Additionally, we show that our method enables us to scale to high dimensional tasks on nontrivial manifolds. In particular, we model QCD densities on SU(n) lattices and contrastively learned embeddings on high dimensional hyperspheres.

We theoretically identify the noise-induced coherent contribution to the ergotropy of a four-level quantum heat engine coupled to a unimodal quantum cavity. We utilize a protocol where the passive state's quasiprobabilities can be analytically identified from the population-coherence coupled reduced density matrix. The reduced density matrix elements are evaluated using a microscopic quantum master equation formalism. Multiple ergotropies within the same coherence interval, each characterized by a positive and pronounced coherent contribution, are observed. These ergotropies are a result of population inversion as well as quasiprobability-population inversion, controllable through the coherence measure parameters. The optimal flux and power of the engine are found to be at moderate values of ergotropy with increasing values of noise-induced coherence. The optimal power at different coherences is found to possess a constant ergotropy.

In recent years, machine learning models like DALL-E, Craiyon, and Stable Diffusion have gained significant attention for their ability to generate high-resolution images from concise descriptions. Concurrently, quantum computing is showing promising advances, especially with quantum machine learning which capitalizes on quantum mechanics to meet the increasing computational requirements of traditional machine learning algorithms. This paper explores the integration of quantum machine learning and variational quantum circuits to augment the efficacy of diffusion-based image generation models. Specifically, we address two challenges of classical diffusion models: their low sampling speed and the extensive parameter requirements. We introduce two quantum diffusion models and benchmark their capabilities against their classical counterparts using MNIST digits, Fashion MNIST, and CIFAR-10. Our models surpass the classical models with similar parameter counts in terms of performance metrics FID, SSIM, and PSNR. Moreover, we introduce a consistency model unitary single sampling architecture that combines the diffusion procedure into a single step, enabling a fast one-step image generation.

Diffusion-based stylization methods typically denoise from a specific partial noise state for image-to-image and video-to-video tasks. This multi-step diffusion process is computationally expensive and hinders real-world application. A promising solution to speed up the process is to obtain few-step consistency models through trajectory distillation. However, current consistency models only force the initial-step alignment between the probability flow ODE (PF-ODE) trajectories of the student and the imperfect teacher models. This training strategy can not ensure the consistency of whole trajectories. To address this issue, we propose single trajectory distillation (STD) starting from a specific partial noise state. We introduce a trajectory bank to store the teacher model's trajectory states, mitigating the time cost during training. Besides, we use an asymmetric adversarial loss to enhance the style and quality of the generated images. Extensive experiments on image and video stylization demonstrate that our method surpasses existing acceleration models in terms of style similarity and aesthetic evaluations. Our code and results will be available on the project page: https://single-trajectory-distillation.github.io.

A theoretical approach to describing transport of an entire ensemble of clusters with different sizes as a single species in gas has been developed. The major assumption is an existence of local partial chemical equilibrium between the clusters. It is shown that thermal diffusion emerges in the collective description as a significant factor even if it is negligible when transport of the original molecular species is considered. Analytical expressions for the effective diffusion and thermal diffusion coefficients at temperature, pressure, and chemical composition gradients have been derived. The theory has been applied to a technology of H2S conversion in a centrifugal plasma-chemical reactor and has made it possible to account for sulfur clusters in numerical process modeling.

Diffusion models have achieved remarkable success in image generation tasks, yet their practical deployment is restrained by the high memory and time consumption. While quantization paves a way for diffusion model compression and acceleration, existing methods totally fail when the models are quantized to low-bits. In this paper, we unravel three properties in quantized diffusion models that compromise the efficacy of current methods: imbalanced activation distributions, imprecise temporal information, and vulnerability to perturbations of specific modules. To alleviate the intensified low-bit quantization difficulty stemming from the distribution imbalance, we propose finetuning the quantized model to better adapt to the activation distribution. Building on this idea, we identify two critical types of quantized layers: those holding vital temporal information and those sensitive to reduced bit-width, and finetune them to mitigate performance degradation with efficiency. We empirically verify that our approach modifies the activation distribution and provides meaningful temporal information, facilitating easier and more accurate quantization. Our method is evaluated over three high-resolution image generation tasks and achieves state-of-the-art performance under various bit-width settings, as well as being the first method to generate readable images on full 4-bit (i.e. W4A4) Stable Diffusion. Code is been made publicly available.

We present a comprehensive numerical study of a six-state clock model with a long-range dipolar type interaction. This model is motivated by the ferroelectric orders in the multiferroic hexagonal manganites. At low temperatures, trimerization of local atomic structures leads to six distinct but energetically degenerate structural distortion, which can be modeled by a six-state clock model. Moreover, the atomic displacements in the trimerized state further produce a local electric polarization whose sign depends on whether the clock variable is even or odd. These induced electric dipoles, which can be modeled by emergent Ising degrees of freedom, interact with each other via long-range dipolar interactions. Extensive Monte Carlo simulations are carried out to investigate low temperature phases resulting from the competing interactions. Upon lowering temperature, the system undergoes two Berezinskii-Kosterlitz-Thouless (BKT) transitions, characteristic of the standard six-state clock model in two dimensions. The dipolar interaction between emergent Ising spins induces a first-order transition into a ground state characterized by a three-fold degenerate stripe order. The intermediate phase between the discontinuous and the second BKT transition corresponds to a maze-like hexagonal liquid with short-range stripe ordering. Moreover, this intermediate phase also exhibits an unusual ferromagnetic order with two adjacent clock variables occupying the two types of stripes of the labyrinthine pattern.

Recently, diffusion models have made remarkable progress in text-to-image (T2I) generation, synthesizing images with high fidelity and diverse contents. Despite this advancement, latent space smoothness within diffusion models remains largely unexplored. Smooth latent spaces ensure that a perturbation on an input latent corresponds to a steady change in the output image. This property proves beneficial in downstream tasks, including image interpolation, inversion, and editing. In this work, we expose the non-smoothness of diffusion latent spaces by observing noticeable visual fluctuations resulting from minor latent variations. To tackle this issue, we propose Smooth Diffusion, a new category of diffusion models that can be simultaneously high-performing and smooth. Specifically, we introduce Step-wise Variation Regularization to enforce the proportion between the variations of an arbitrary input latent and that of the output image is a constant at any diffusion training step. In addition, we devise an interpolation standard deviation (ISTD) metric to effectively assess the latent space smoothness of a diffusion model. Extensive quantitative and qualitative experiments demonstrate that Smooth Diffusion stands out as a more desirable solution not only in T2I generation but also across various downstream tasks. Smooth Diffusion is implemented as a plug-and-play Smooth-LoRA to work with various community models. Code is available at https://github.com/SHI-Labs/Smooth-Diffusion.

The latent space of diffusion model mostly still remains unexplored, despite its great success and potential in the field of generative modeling. In fact, the latent space of existing diffusion models are entangled, with a distorted mapping from its latent space to image space. To tackle this problem, we present Isometric Diffusion, equipping a diffusion model with a geometric regularizer to guide the model to learn a geometrically sound latent space of the training data manifold. This approach allows diffusion models to learn a more disentangled latent space, which enables smoother interpolation, more accurate inversion, and more precise control over attributes directly in the latent space. Our extensive experiments consisting of image interpolations, image inversions, and linear editing show the effectiveness of our method.

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.

This monograph presents the core principles that have guided the development of diffusion models, tracing their origins and showing how diverse formulations arise from shared mathematical ideas. Diffusion modeling starts by defining a forward process that gradually corrupts data into noise, linking the data distribution to a simple prior through a continuum of intermediate distributions. The goal is to learn a reverse process that transforms noise back into data while recovering the same intermediates. We describe three complementary views. The variational view, inspired by variational autoencoders, sees diffusion as learning to remove noise step by step. The score-based view, rooted in energy-based modeling, learns the gradient of the evolving data distribution, indicating how to nudge samples toward more likely regions. The flow-based view, related to normalizing flows, treats generation as following a smooth path that moves samples from noise to data under a learned velocity field. These perspectives share a common backbone: a time-dependent velocity field whose flow transports a simple prior to the data. Sampling then amounts to solving a differential equation that evolves noise into data along a continuous trajectory. On this foundation, the monograph discusses guidance for controllable generation, efficient numerical solvers, and diffusion-motivated flow-map models that learn direct mappings between arbitrary times. It provides a conceptual and mathematically grounded understanding of diffusion models for readers with basic deep-learning knowledge.

We introduce a technique for extracting microstructural geometry from NMR lineshape analysis in porous materials at angstrom-scale resolution with the use of weak magnetic field gradients. Diverging from the generally held view of FID signals undergoing simple exponential decay, we show that a detailed analysis of the line shape can unravel structural geometry on much smaller scales than previously thought. While the original q-space PFG NMR relies on strong magnetic field gradients in order to achieve high spatial resolution, our current approach reaches comparable or higher resolution using much weaker gradients. As a model system, we simulated gas diffusion for xenon confined within carbon nanotubes over a range of temperatures and nanotube diameters in order to unveil manifestations of confinement in the diffusion behavior. We report a multiscale scheme that couples the above MD simulations with the generalized Langevin equation to estimate the transport properties of interest for this problem, such as diffusivity coefficients and NMR lineshapes, using the Green-Kubo correlation function to correctly evaluate time-dependent diffusion. Our results highlight how NMR methodologies can be adapted as effective means towards structural investigation at very small scales when dealing with complicated geometries. This method is expected to find applications in materials science, catalysis, biomedicine and other areas.

Infrared imaging technology has gained significant attention for its reliable sensing ability in low visibility conditions, prompting many studies to convert the abundant RGB images to infrared images. However, most existing image translation methods treat infrared images as a stylistic variation, neglecting the underlying physical laws, which limits their practical application. To address these issues, we propose a Physics-Informed Diffusion (PID) model for translating RGB images to infrared images that adhere to physical laws. Our method leverages the iterative optimization of the diffusion model and incorporates strong physical constraints based on prior knowledge of infrared laws during training. This approach enhances the similarity between translated infrared images and the real infrared domain without increasing extra training parameters. Experimental results demonstrate that PID significantly outperforms existing state-of-the-art methods. Our code is available at https://github.com/fangyuanmao/PID.

We investigate equilibration and generalized thermalization of the quantum Harmonic chain under local quantum quench. The quench action we consider is connecting two disjoint harmonic chains of different sizes and the system jumps between two integrable settings. We verify the validity of the Generalized Gibbs Ensemble description for this infinite dimensional Hilbert space system and also identify equilibration between the subsystems as in classical systems. Using Bogoliubov transformations, we show that the eigenstates of the system prior to the quench evolve towards the Gibbs Generalized Ensemble description. Eigenstates that are more delocalized (in the sense of inverse participation ratio) prior to the quench, tend to equilibrate more rapidly. Further, through the phase space properties of a Generalized Gibbs Ensemble and the strength of stimulated emission, we identify the necessary criterion on the initial states for such relaxation at late times and also find out the states which would potentially not be described by the Gibbs Generalized Ensemble description.

Simulating and controlling physical systems described by partial differential equations (PDEs) are crucial tasks across science and engineering. Recently, diffusion generative models have emerged as a competitive class of methods for these tasks due to their ability to capture long-term dependencies and model high-dimensional states. However, diffusion models typically struggle with handling system states with abrupt changes and generalizing to higher resolutions. In this work, we propose Wavelet Diffusion Neural Operator (WDNO), a novel PDE simulation and control framework that enhances the handling of these complexities. WDNO comprises two key innovations. Firstly, WDNO performs diffusion-based generative modeling in the wavelet domain for the entire trajectory to handle abrupt changes and long-term dependencies effectively. Secondly, to address the issue of poor generalization across different resolutions, which is one of the fundamental tasks in modeling physical systems, we introduce multi-resolution training. We validate WDNO on five physical systems, including 1D advection equation, three challenging physical systems with abrupt changes (1D Burgers' equation, 1D compressible Navier-Stokes equation and 2D incompressible fluid), and a real-world dataset ERA5, which demonstrates superior performance on both simulation and control tasks over state-of-the-art methods, with significant improvements in long-term and detail prediction accuracy. Remarkably, in the challenging context of the 2D high-dimensional and indirect control task aimed at reducing smoke leakage, WDNO reduces the leakage by 33.2% compared to the second-best baseline. The code can be found at https://github.com/AI4Science-WestlakeU/wdno.git.

Diffusion models have advanced from text-to-image (T2I) to image-to-image (I2I) generation by incorporating structured inputs such as depth maps, enabling fine-grained spatial control. However, existing methods either train separate models for each condition or rely on unified architectures with entangled representations, resulting in poor generalization and high adaptation costs for novel conditions. To this end, we propose DivControl, a decomposable pretraining framework for unified controllable generation and efficient adaptation. DivControl factorizes ControlNet via SVD into basic components-pairs of singular vectors-which are disentangled into condition-agnostic learngenes and condition-specific tailors through knowledge diversion during multi-condition training. Knowledge diversion is implemented via a dynamic gate that performs soft routing over tailors based on the semantics of condition instructions, enabling zero-shot generalization and parameter-efficient adaptation to novel conditions. To further improve condition fidelity and training efficiency, we introduce a representation alignment loss that aligns condition embeddings with early diffusion features. Extensive experiments demonstrate that DivControl achieves state-of-the-art controllability with 36.4times less training cost, while simultaneously improving average performance on basic conditions. It also delivers strong zero-shot and few-shot performance on unseen conditions, demonstrating superior scalability, modularity, and transferability.

Diffusion Policies have demonstrated impressive performance in robotic manipulation tasks. However, their long inference time, resulting from an extensive iterative denoising process, and the need to execute an action chunk before the next prediction to maintain consistent actions limit their applicability to latency-critical tasks or simple tasks with a short cycle time. While recent methods explored distillation or alternative policy structures to accelerate inference, these often demand additional training, which can be resource-intensive for large robotic models. In this paper, we introduce a novel approach inspired by the Real-Time Iteration (RTI) Scheme, a method from optimal control that accelerates optimization by leveraging solutions from previous time steps as initial guesses for subsequent iterations. We explore the application of this scheme in diffusion inference and propose a scaling-based method to effectively handle discrete actions, such as grasping, in robotic manipulation. The proposed scheme significantly reduces runtime computational costs without the need for distillation or policy redesign. This enables a seamless integration into many pre-trained diffusion-based models, in particular, to resource-demanding large models. We also provide theoretical conditions for the contractivity which could be useful for estimating the initial denoising step. Quantitative results from extensive simulation experiments show a substantial reduction in inference time, with comparable overall performance compared with Diffusion Policy using full-step denoising. Our project page with additional resources is available at: https://rti-dp.github.io/.

Large-scale, pre-trained Text-to-Image (T2I) diffusion models have gained significant popularity in image generation tasks and have shown unexpected potential in image Super-Resolution (SR). However, most existing T2I diffusion models are trained with a resolution limit of 512x512, making scaling beyond this resolution an unresolved but necessary challenge for image SR. In this work, we introduce a novel approach that, for the first time, enables these models to generate 2K, 4K, and even 8K images without any additional training. Our method leverages MultiDiffusion, which distributes the generation across multiple diffusion paths to ensure global coherence at larger scales, and local degradation-aware prompt extraction, which guides the T2I model to reconstruct fine local structures according to its low-resolution input. These innovations unlock higher resolutions, allowing T2I diffusion models to be applied to image SR tasks without limitation on resolution.

Let L denote the Laplacian matrix of a graph G. We study continuous quantum walks on G defined by the transition matrix U(t)=expleft(itLright). The initial state is of the pair state form, e_a-e_b with a,b being any two vertices of G. We provide two ways to construct infinite families of graphs that have perfect pair transfer. We study a "transitivity" phenomenon which cannot occur in vertex state transfer. We characterize perfect pair state transfer on paths and cycles. We also study the case when quantum walks are generated by the unsigned Laplacians of underlying graphs and the initial states are of the plus state form, e_a+e_b. When the underlying graphs are bipartite, plus state transfer is equivalent to pair state transfer.

Recent advances in diffusion models have shown remarkable potential in the conditional generation of novel molecules. These models can be guided in two ways: (i) explicitly, through additional features representing the condition, or (ii) implicitly, using a property predictor. However, training property predictors or conditional diffusion models requires an abundance of labeled data and is inherently challenging in real-world applications. We propose a novel approach that attenuates the limitations of acquiring large labeled datasets by leveraging domain knowledge from quantum chemistry as a non-differentiable oracle to guide an unconditional diffusion model. Instead of relying on neural networks, the oracle provides accurate guidance in the form of estimated gradients, allowing the diffusion process to sample from a conditional distribution specified by quantum chemistry. We show that this results in more precise conditional generation of novel and stable molecular structures. Our experiments demonstrate that our method: (1) significantly reduces atomic forces, enhancing the validity of generated molecules when used for stability optimization; (2) is compatible with both explicit and implicit guidance in diffusion models, enabling joint optimization of molecular properties and stability; and (3) generalizes effectively to molecular optimization tasks beyond stability optimization.

Denoising diffusion probabilistic models have recently received much research attention since they outperform alternative approaches, such as GANs, and currently provide state-of-the-art generative performance. The superior performance of diffusion models has made them an appealing tool in several applications, including inpainting, super-resolution, and semantic editing. In this paper, we demonstrate that diffusion models can also serve as an instrument for semantic segmentation, especially in the setup when labeled data is scarce. In particular, for several pretrained diffusion models, we investigate the intermediate activations from the networks that perform the Markov step of the reverse diffusion process. We show that these activations effectively capture the semantic information from an input image and appear to be excellent pixel-level representations for the segmentation problem. Based on these observations, we describe a simple segmentation method, which can work even if only a few training images are provided. Our approach significantly outperforms the existing alternatives on several datasets for the same amount of human supervision.

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.

Image denoising is a fundamental problem in computational photography, where achieving high perception with low distortion is highly demanding. Current methods either struggle with perceptual quality or suffer from significant distortion. Recently, the emerging diffusion model has achieved state-of-the-art performance in various tasks and demonstrates great potential for image denoising. However, stimulating diffusion models for image denoising is not straightforward and requires solving several critical problems. For one thing, the input inconsistency hinders the connection between diffusion models and image denoising. For another, the content inconsistency between the generated image and the desired denoised image introduces distortion. To tackle these problems, we present a novel strategy called the Diffusion Model for Image Denoising (DMID) by understanding and rethinking the diffusion model from a denoising perspective. Our DMID strategy includes an adaptive embedding method that embeds the noisy image into a pre-trained unconditional diffusion model and an adaptive ensembling method that reduces distortion in the denoised image. Our DMID strategy achieves state-of-the-art performance on both distortion-based and perception-based metrics, for both Gaussian and real-world image denoising.The code is available at https://github.com/Li-Tong-621/DMID.

Diffusion-based generative models' impressive ability to create convincing images has captured global attention. However, their complex internal structures and operations often make them difficult for non-experts to understand. We present Diffusion Explainer, the first interactive visualization tool that explains how Stable Diffusion transforms text prompts into images. Diffusion Explainer tightly integrates a visual overview of Stable Diffusion's complex components with detailed explanations of their underlying operations, enabling users to fluidly transition between multiple levels of abstraction through animations and interactive elements. By comparing the evolutions of image representations guided by two related text prompts over refinement timesteps, users can discover the impact of prompts on image generation. Diffusion Explainer runs locally in users' web browsers without the need for installation or specialized hardware, broadening the public's education access to modern AI techniques. Our open-sourced tool is available at: https://poloclub.github.io/diffusion-explainer/.

Deep generative diffusion models are a promising avenue for 3D de novo molecular design in materials science and drug discovery. However, their utility is still limited by suboptimal performance on large molecular structures and limited training data. To address this gap, we explore the design space of E(3)-equivariant diffusion models, focusing on previously unexplored areas. Our extensive comparative analysis evaluates the interplay between continuous and discrete state spaces. From this investigation, we present the EQGAT-diff model, which consistently outperforms established models for the QM9 and GEOM-Drugs datasets. Significantly, EQGAT-diff takes continuous atom positions, while chemical elements and bond types are categorical and uses time-dependent loss weighting, substantially increasing training convergence, the quality of generated samples, and inference time. We also showcase that including chemically motivated additional features like hybridization states in the diffusion process enhances the validity of generated molecules. To further strengthen the applicability of diffusion models to limited training data, we investigate the transferability of EQGAT-diff trained on the large PubChem3D dataset with implicit hydrogen atoms to target different data distributions. Fine-tuning EQGAT-diff for just a few iterations shows an efficient distribution shift, further improving performance throughout data sets. Finally, we test our model on the Crossdocked data set for structure-based de novo ligand generation, underlining the importance of our findings showing state-of-the-art performance on Vina docking scores.

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.

Diffusion models have exhibited excellent performance in various domains. The probability flow ordinary differential equation (ODE) of diffusion models (i.e., diffusion ODEs) is a particular case of continuous normalizing flows (CNFs), which enables deterministic inference and exact likelihood evaluation. However, the likelihood estimation results by diffusion ODEs are still far from those of the state-of-the-art likelihood-based generative models. In this work, we propose several improved techniques for maximum likelihood estimation for diffusion ODEs, including both training and evaluation perspectives. For training, we propose velocity parameterization and explore variance reduction techniques for faster convergence. We also derive an error-bounded high-order flow matching objective for finetuning, which improves the ODE likelihood and smooths its trajectory. For evaluation, we propose a novel training-free truncated-normal dequantization to fill the training-evaluation gap commonly existing in diffusion ODEs. Building upon these techniques, we achieve state-of-the-art likelihood estimation results on image datasets (2.56 on CIFAR-10, 3.43/3.69 on ImageNet-32) without variational dequantization or data augmentation.

Diffusion models have achieved remarkable success in the domain of text-guided image generation and, more recently, in text-guided image editing. A commonly adopted strategy for editing real images involves inverting the diffusion process to obtain a noisy representation of the original image, which is then denoised to achieve the desired edits. However, current methods for diffusion inversion often struggle to produce edits that are both faithful to the specified text prompt and closely resemble the source image. To overcome these limitations, we introduce a novel and adaptable diffusion inversion technique for real image editing, which is grounded in a theoretical analysis of the role of eta in the DDIM sampling equation for enhanced editability. By designing a universal diffusion inversion method with a time- and region-dependent eta function, we enable flexible control over the editing extent. Through a comprehensive series of quantitative and qualitative assessments, involving a comparison with a broad array of recent methods, we demonstrate the superiority of our approach. Our method not only sets a new benchmark in the field but also significantly outperforms existing strategies.

Recent advancements in video diffusion models have significantly enhanced audio-driven portrait animation. However, current methods still suffer from flickering, identity drift, and poor audio-visual synchronization. These issues primarily stem from entangled appearance-motion representations and unstable inference strategies. In this paper, we introduce ConsistTalk, a novel intensity-controllable and temporally consistent talking head generation framework with diffusion noise search inference. First, we propose an optical flow-guided temporal module (OFT) that decouples motion features from static appearance by leveraging facial optical flow, thereby reducing visual flicker and improving temporal consistency. Second, we present an Audio-to-Intensity (A2I) model obtained through multimodal teacher-student knowledge distillation. By transforming audio and facial velocity features into a frame-wise intensity sequence, the A2I model enables joint modeling of audio and visual motion, resulting in more natural dynamics. This further enables fine-grained, frame-wise control of motion dynamics while maintaining tight audio-visual synchronization. Third, we introduce a diffusion noise initialization strategy (IC-Init). By enforcing explicit constraints on background coherence and motion continuity during inference-time noise search, we achieve better identity preservation and refine motion dynamics compared to the current autoregressive strategy. Extensive experiments demonstrate that ConsistTalk significantly outperforms prior methods in reducing flicker, preserving identity, and delivering temporally stable, high-fidelity talking head videos.

In 2000, Gillespie rehabilitated the chemical Langevin equation (CLE) by describing two conditions that must be satisfied for it yield a valid approximation of the chemical master equation (CME). In this work, we construct an original path integral description of the CME, and show how applying Gillespie's two conditions to it directly leads to a path integral equivalent to the CLE. We compare this approach to the path integral equivalent of a large system size derivation, and show that they are qualitatively different. In particular, both approaches involve converting many sums into many integrals, and the difference between the two methods is essentially the difference between using the Euler-Maclaurin formula and using Riemann sums. Our results shed light on how path integrals can be used to conceptualize coarse-graining biochemical systems, and are readily generalizable.

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 quickly risen in popularity for their ability to model complex distributions and perform effective posterior sampling. Unfortunately, the iterative nature of these generative models makes them computationally expensive and unsuitable for real-time sequential inverse problems such as ultrasound imaging. Considering the strong temporal structure across sequences of frames, we propose a novel approach that models the transition dynamics to improve the efficiency of sequential diffusion posterior sampling in conditional image synthesis. Through modeling sequence data using a video vision transformer (ViViT) transition model based on previous diffusion outputs, we can initialize the reverse diffusion trajectory at a lower noise scale, greatly reducing the number of iterations required for convergence. We demonstrate the effectiveness of our approach on a real-world dataset of high frame rate cardiac ultrasound images and show that it achieves the same performance as a full diffusion trajectory while accelerating inference 25times, enabling real-time posterior sampling. Furthermore, we show that the addition of a transition model improves the PSNR up to 8\% in cases with severe motion. Our method opens up new possibilities for real-time applications of diffusion models in imaging and other domains requiring real-time inference.

Diffusion models are emerging models that generate images by iteratively denoising random Gaussian noise using deep neural networks. These models typically exhibit high computational and memory demands, necessitating effective post-training quantization for high-performance inference. Recent works propose low-bitwidth (e.g., 8-bit or 4-bit) quantization for diffusion models, however 4-bit integer quantization typically results in low-quality images. We observe that on several widely used hardware platforms, there is little or no difference in compute capability between floating-point and integer arithmetic operations of the same bitwidth (e.g., 8-bit or 4-bit). Therefore, we propose an effective floating-point quantization method for diffusion models that provides better image quality compared to integer quantization methods. We employ a floating-point quantization method that was effective for other processing tasks, specifically computer vision and natural language tasks, and tailor it for diffusion models by integrating weight rounding learning during the mapping of the full-precision values to the quantized values in the quantization process. We comprehensively study integer and floating-point quantization methods in state-of-the-art diffusion models. Our floating-point quantization method not only generates higher-quality images than that of integer quantization methods, but also shows no noticeable degradation compared to full-precision models (32-bit floating-point), when both weights and activations are quantized to 8-bit floating-point values, while has minimal degradation with 4-bit weights and 8-bit activations.

Large diffusion-based Text-to-Image (T2I) models have shown impressive generative powers for text-to-image generation as well as spatially conditioned image generation. For most applications, we can train the model end-toend with paired data to obtain photorealistic generation quality. However, to add an additional task, one often needs to retrain the model from scratch using paired data across all modalities to retain good generation performance. In this paper, we tackle this issue and propose a novel strategy to scale a generative model across new tasks with minimal compute. During our experiments, we discovered that the variance maps of intermediate feature maps of diffusion models capture the intensity of conditioning. Utilizing this prior information, we propose MaxFusion, an efficient strategy to scale up text-to-image generation models to accommodate new modality conditions. Specifically, we combine aligned features of multiple models, hence bringing a compositional effect. Our fusion strategy can be integrated into off-the-shelf models to enhance their generative prowess.

Understanding transition pathways between two meta-stable states of a molecular system is crucial to advance drug discovery and material design. However, unbiased molecular dynamics (MD) simulations are computationally infeasible because of the high energy barriers that separate these states. Although recent machine learning techniques are proposed to sample rare events, they are often limited to simple systems and rely on collective variables (CVs) derived from costly domain expertise. In this paper, we introduce a novel approach that trains diffusion path samplers (DPS) to address the transition path sampling (TPS) problem without requiring CVs. We reformulate the problem as an amortized sampling from the transition path distribution by minimizing the log-variance divergence between the path distribution induced by DPS and the transition path distribution. Based on the log-variance divergence, we propose learnable control variates to reduce the variance of gradient estimators and the off-policy training objective with replay buffers and simulated annealing techniques to improve sample efficiency and diversity. We also propose a scale-based equivariant parameterization of the bias forces to ensure scalability for large systems. We extensively evaluate our approach, termed TPS-DPS, on a synthetic system, small peptide, and challenging fast-folding proteins, demonstrating that it produces more realistic and diverse transition pathways than existing baselines.

While diffusion-based image restoration (IR) methods have achieved remarkable success, they are still limited by the low inference speed attributed to the necessity of executing hundreds or even thousands of sampling steps. Existing acceleration sampling techniques, though seeking to expedite the process, inevitably sacrifice performance to some extent, resulting in over-blurry restored outcomes. To address this issue, this study proposes a novel and efficient diffusion model for IR that significantly reduces the required number of diffusion steps. Our method avoids the need for post-acceleration during inference, thereby avoiding the associated performance deterioration. Specifically, our proposed method establishes a Markov chain that facilitates the transitions between the high-quality and low-quality images by shifting their residuals, substantially improving the transition efficiency. A carefully formulated noise schedule is devised to flexibly control the shifting speed and the noise strength during the diffusion process. Extensive experimental evaluations demonstrate that the proposed method achieves superior or comparable performance to current state-of-the-art methods on three classical IR tasks, namely image super-resolution, image inpainting, and blind face restoration, \textbf{even only with four sampling steps}. Our code and model are publicly available at https://github.com/zsyOAOA/ResShift.

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

Diffusion distillation represents a highly promising direction for achieving faithful text-to-image generation in a few sampling steps. However, despite recent successes, existing distilled models still do not provide the full spectrum of diffusion abilities, such as real image inversion, which enables many precise image manipulation methods. This work aims to enrich distilled text-to-image diffusion models with the ability to effectively encode real images into their latent space. To this end, we introduce invertible Consistency Distillation (iCD), a generalized consistency distillation framework that facilitates both high-quality image synthesis and accurate image encoding in only 3-4 inference steps. Though the inversion problem for text-to-image diffusion models gets exacerbated by high classifier-free guidance scales, we notice that dynamic guidance significantly reduces reconstruction errors without noticeable degradation in generation performance. As a result, we demonstrate that iCD equipped with dynamic guidance may serve as a highly effective tool for zero-shot text-guided image editing, competing with more expensive state-of-the-art alternatives.

To accelerate diffusion model inference, numerical solvers perform poorly at extremely small steps, while distillation techniques often introduce complexity and instability. This work presents an intermediate strategy, balancing performance and cost, by learning ODE integration using loss functions derived from the derivative-integral relationship, inspired by Monte Carlo integration and Picard iteration. From a geometric perspective, the losses operate by gradually extending the tangent to the secant, thus are named as secant losses. The target of secant losses is the same as that of diffusion models, or the diffusion model itself, leading to great training stability. By fine-tuning or distillation, the secant version of EDM achieves a 10-step FID of 2.14 on CIFAR-10, while the secant version of SiT-XL/2 attains a 4-step FID of 2.27 and an 8-step FID of 1.96 on ImageNet-256times256. Code is available at https://github.com/poppuppy/secant-expectation.

We show how to extract from a sufficiently long time series of stationary fluctuations of chemical reactions an estimate of the entropy production. This method, which is based on recent work on fluctuation theorems, is direct, non-invasive, does not require any knowledge about the underlying dynamics, and is applicable even when only partial information is available. We apply it to simple stochastic models of chemical reactions involving a finite number of states, and for this case, we study how the estimate of dissipation is affected by the degree of coarse-graining present in the input data.

Chemical potential of species in solution is essential for understanding various chemical processes at interfaces. Molecular dynamics (MD) simulations, constrained by fixed compositions, cannot satisfy a constant chemical potential condition as solute species can migrate to the interface and deplete the bulk due to solute-interface interactions. In this study, we introduce a simple and computationally efficient approach named iterative constant chemical potential molecular dynamics (iCuMD) simulation, which helps simulate targeted molar concentrations of species in solution. iCuMD overcomes the limitations of conventional MD by adjusting the number of species in the solution to reach a target concentration (chemical potential). We demonstrate our approach using solid-liquid and liquid-air interfacial systems as case studies. Specifically, we perform classical force field-based MD simulations of NaCl(aq)-air and NaCl(aq)-graphite interfaces and machine learning interatomic potential (MLIP)-based MD simulations of the Na2SO4(aq)-graphene interface. Our results show that the iCuMD approach efficiently achieves the desired bulk ion concentration within two iterations and can also be integrated with MLIP-driven simulations which enable constant potential simulations with DFT-level accuracy. We show that iCuMD offers a robust and simple computational framework for constant chemical potential simulations as its only requirement is to be able to converge interfacial simulations with a measurable bulk region.

Diffusion-based image generators can now produce high-quality and diverse samples, but their success has yet to fully translate to 3D generation: existing diffusion methods can either generate low-resolution but 3D consistent outputs, or detailed 2D views of 3D objects but with potential structural defects and lacking view consistency or realism. We present HoloFusion, a method that combines the best of these approaches to produce high-fidelity, plausible, and diverse 3D samples while learning from a collection of multi-view 2D images only. The method first generates coarse 3D samples using a variant of the recently proposed HoloDiffusion generator. Then, it independently renders and upsamples a large number of views of the coarse 3D model, super-resolves them to add detail, and distills those into a single, high-fidelity implicit 3D representation, which also ensures view consistency of the final renders. The super-resolution network is trained as an integral part of HoloFusion, end-to-end, and the final distillation uses a new sampling scheme to capture the space of super-resolved signals. We compare our method against existing baselines, including DreamFusion, Get3D, EG3D, and HoloDiffusion, and achieve, to the best of our knowledge, the most realistic results on the challenging CO3Dv2 dataset.

We introduce a novel framework for efficient sampling from complex, unnormalised target distributions by exploiting multiscale dynamics. Traditional score-based sampling methods either rely on learned approximations of the score function or involve computationally expensive nested Markov chain Monte Carlo (MCMC) loops. In contrast, the proposed approach leverages stochastic averaging within a slow-fast system of stochastic differential equations (SDEs) to estimate intermediate scores along a diffusion path without training or inner-loop MCMC. Two algorithms are developed under this framework: MultALMC, which uses multiscale annealed Langevin dynamics, and MultCDiff, based on multiscale controlled diffusions for the reverse-time Ornstein-Uhlenbeck process. Both overdamped and underdamped variants are considered, with theoretical guarantees of convergence to the desired diffusion path. The framework is extended to handle heavy-tailed target distributions using Student's t-based noise models and tailored fast-process dynamics. Empirical results across synthetic and real-world benchmarks, including multimodal and high-dimensional distributions, demonstrate that the proposed methods are competitive with existing samplers in terms of accuracy and efficiency, without the need for learned models.

The slow inference process of image diffusion models significantly degrades interactive user experiences. To address this, we introduce Diffusion Preview, a novel paradigm employing rapid, low-step sampling to generate preliminary outputs for user evaluation, deferring full-step refinement until the preview is deemed satisfactory. Existing acceleration methods, including training-free solvers and post-training distillation, struggle to deliver high-quality previews or ensure consistency between previews and final outputs. We propose ConsistencySolver derived from general linear multistep methods, a lightweight, trainable high-order solver optimized via Reinforcement Learning, that enhances preview quality and consistency. Experimental results demonstrate that ConsistencySolver significantly improves generation quality and consistency in low-step scenarios, making it ideal for efficient preview-and-refine workflows. Notably, it achieves FID scores on-par with Multistep DPM-Solver using 47% fewer steps, while outperforming distillation baselines. Furthermore, user studies indicate our approach reduces overall user interaction time by nearly 50% while maintaining generation quality. Code is available at https://github.com/G-U-N/consolver.

Diffusion models (DMs) have been adopted across diverse fields with its remarkable abilities in capturing intricate data distributions. In this paper, we propose a Fast Diffusion Model (FDM) to significantly speed up DMs from a stochastic optimization perspective for both faster training and sampling. We first find that the diffusion process of DMs accords with the stochastic optimization process of stochastic gradient descent (SGD) on a stochastic time-variant problem. Then, inspired by momentum SGD that uses both gradient and an extra momentum to achieve faster and more stable convergence than SGD, we integrate momentum into the diffusion process of DMs. This comes with a unique challenge of deriving the noise perturbation kernel from the momentum-based diffusion process. To this end, we frame the process as a Damped Oscillation system whose critically damped state -- the kernel solution -- avoids oscillation and yields a faster convergence speed of the diffusion process. Empirical results show that our FDM can be applied to several popular DM frameworks, e.g., VP, VE, and EDM, and reduces their training cost by about 50% with comparable image synthesis performance on CIFAR-10, FFHQ, and AFHQv2 datasets. Moreover, FDM decreases their sampling steps by about 3x to achieve similar performance under the same samplers. The code is available at https://github.com/sail-sg/FDM.

The substantial training cost of diffusion models hinders their deployment. Immiscible Diffusion recently showed that reducing diffusion trajectory mixing in the noise space via linear assignment accelerates training by simplifying denoising. To extend immiscible diffusion beyond the inefficient linear assignment under high batch sizes and high dimensions, we refine this concept to a broader miscibility reduction at any layer and by any implementation. Specifically, we empirically demonstrate the bijective nature of the denoising process with respect to immiscible diffusion, ensuring its preservation of generative diversity. Moreover, we provide thorough analysis and show step-by-step how immiscibility eases denoising and improves efficiency. Extending beyond linear assignment, we propose a family of implementations including K-nearest neighbor (KNN) noise selection and image scaling to reduce miscibility, achieving up to >4x faster training across diverse models and tasks including unconditional/conditional generation, image editing, and robotics planning. Furthermore, our analysis of immiscibility offers a novel perspective on how optimal transport (OT) enhances diffusion training. By identifying trajectory miscibility as a fundamental bottleneck, we believe this work establishes a potentially new direction for future research into high-efficiency diffusion training. The code is available at https://github.com/yhli123/Immiscible-Diffusion.

Diffusion-based image restoration (IR) methods aim to use diffusion models to recover high-quality (HQ) images from degraded images and achieve promising performance. Due to the inherent property of diffusion models, most of these methods need long serial sampling chains to restore HQ images step-by-step. As a result, it leads to expensive sampling time and high computation costs. Moreover, such long sampling chains hinder understanding the relationship between the restoration results and the inputs since it is hard to compute the gradients in the whole chains. In this work, we aim to rethink the diffusion-based IR models through a different perspective, i.e., a deep equilibrium (DEQ) fixed point system. Specifically, we derive an analytical solution by modeling the entire sampling chain in diffusion-based IR models as a joint multivariate fixed point system. With the help of the analytical solution, we are able to conduct single-image sampling in a parallel way and restore HQ images without training. Furthermore, we compute fast gradients in DEQ and found that initialization optimization can boost performance and control the generation direction. Extensive experiments on benchmarks demonstrate the effectiveness of our proposed method on typical IR tasks and real-world settings. The code and models will be made publicly available.

In an experiment on a turbulent jet, we detect interfacial turbulent layers in a frame that moves, on average, along with the \tnti. This significantly prolongs the observation time of scalar and velocity structures and enables the measurement of two types of Lagrangian coherent structures. One structure, the finite-time Lyapunov field (FTLE), quantifies advective transport barriers of fluid parcels while the other structure highlights barriers of diffusive momentum transport. These two complementary structures depend on large-scale and small-scale motion and are therefore associated with the growth of the turbulent region through engulfment or nibbling, respectively. We detect the \tnti\ from cluster analysis, where we divide the measured scalar field into four clusters. Not only the \tnti\ can be found this way, but also the next, internal, turbulent-turbulent interface. Conditional averages show that these interfaces are correlated with barriers of advective and diffusive transport when the Lagrangian integration time is smaller than the integral time scale. Diffusive structures decorrelate faster since they have a smaller timescale. Conditional averages of these structures at internal turbulent-turbulent interfaces show the same pattern with a more pronounced jump at the interface indicative of a shear layer. This is quite an unexpected outcome, as the internal interface is now defined not by the presence or absence of vorticity, but by conditional vorticity corresponding to two uniform concentration zones. The long-time diffusive momentum flux along Lagrangian paths represents the growth of the turbulent flow into the irrotational domain, a direct demonstration of nibbling. The diffusive flux parallel to the \tnti\ appears to be concentrated in a diffusive superlayer whose width is comparable with the Taylor microscale, which is relatively invariant in time.

Large video diffusion and flow models have achieved remarkable success in high-quality video generation, but their use in real-time interactive applications remains limited due to their inefficient multi-step sampling process. In this work, we present Transition Matching Distillation (TMD), a novel framework for distilling video diffusion models into efficient few-step generators. The central idea of TMD is to match the multi-step denoising trajectory of a diffusion model with a few-step probability transition process, where each transition is modeled as a lightweight conditional flow. To enable efficient distillation, we decompose the original diffusion backbone into two components: (1) a main backbone, comprising the majority of early layers, that extracts semantic representations at each outer transition step; and (2) a flow head, consisting of the last few layers, that leverages these representations to perform multiple inner flow updates. Given a pretrained video diffusion model, we first introduce a flow head to the model, and adapt it into a conditional flow map. We then apply distribution matching distillation to the student model with flow head rollout in each transition step. Extensive experiments on distilling Wan2.1 1.3B and 14B text-to-video models demonstrate that TMD provides a flexible and strong trade-off between generation speed and visual quality. In particular, TMD outperforms existing distilled models under comparable inference costs in terms of visual fidelity and prompt adherence. Project page: https://research.nvidia.com/labs/genair/tmd

We address the challenges of precise image inversion and disentangled image editing in the context of few-step diffusion models. We introduce an encoder based iterative inversion technique. The inversion network is conditioned on the input image and the reconstructed image from the previous step, allowing for correction of the next reconstruction towards the input image. We demonstrate that disentangled controls can be easily achieved in the few-step diffusion model by conditioning on an (automatically generated) detailed text prompt. To manipulate the inverted image, we freeze the noise maps and modify one attribute in the text prompt (either manually or via instruction based editing driven by an LLM), resulting in the generation of a new image similar to the input image with only one attribute changed. It can further control the editing strength and accept instructive text prompt. Our approach facilitates realistic text-guided image edits in real-time, requiring only 8 number of functional evaluations (NFEs) in inversion (one-time cost) and 4 NFEs per edit. Our method is not only fast, but also significantly outperforms state-of-the-art multi-step diffusion editing techniques.

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

Generative diffusion models have emerged as a powerful tool for high-quality image synthesis, yet their iterative nature demands significant computational resources. This paper proposes an efficient time step sampling method based on an image spectral analysis of the diffusion process, aimed at optimizing the denoising process. Instead of the traditional uniform distribution-based time step sampling, we introduce a Beta distribution-like sampling technique that prioritizes critical steps in the early and late stages of the process. Our hypothesis is that certain steps exhibit significant changes in image content, while others contribute minimally. We validated our approach using Fourier transforms to measure frequency response changes at each step, revealing substantial low-frequency changes early on and high-frequency adjustments later. Experiments with ADM and Stable Diffusion demonstrated that our Beta Sampling method consistently outperforms uniform sampling, achieving better FID and IS scores, and offers competitive efficiency relative to state-of-the-art methods like AutoDiffusion. This work provides a practical framework for enhancing diffusion model efficiency by focusing computational resources on the most impactful steps, with potential for further optimization and broader application.

Diffusion models for continuous data gained widespread adoption owing to their high quality generation and control mechanisms. However, controllable diffusion on discrete data faces challenges given that continuous guidance methods do not directly apply to discrete diffusion. Here, we provide a straightforward derivation of classifier-free and classifier-based guidance for discrete diffusion, as well as a new class of diffusion models that leverage uniform noise and that are more guidable because they can continuously edit their outputs. We improve the quality of these models with a novel continuous-time variational lower bound that yields state-of-the-art performance, especially in settings involving guidance or fast generation. Empirically, we demonstrate that our guidance mechanisms combined with uniform noise diffusion improve controllable generation relative to autoregressive and diffusion baselines on several discrete data domains, including genomic sequences, small molecule design, and discretized image generation.

Diffusion models have achieved great success in image synthesis through iterative noise estimation using deep neural networks. However, the slow inference, high memory consumption, and computation intensity of the noise estimation model hinder the efficient adoption of diffusion models. Although post-training quantization (PTQ) is considered a go-to compression method for other tasks, it does not work out-of-the-box on diffusion models. We propose a novel PTQ method specifically tailored towards the unique multi-timestep pipeline and model architecture of the diffusion models, which compresses the noise estimation network to accelerate the generation process. We identify the key difficulty of diffusion model quantization as the changing output distributions of noise estimation networks over multiple time steps and the bimodal activation distribution of the shortcut layers within the noise estimation network. We tackle these challenges with timestep-aware calibration and split shortcut quantization in this work. Experimental results show that our proposed method is able to quantize full-precision unconditional diffusion models into 4-bit while maintaining comparable performance (small FID change of at most 2.34 compared to >100 for traditional PTQ) in a training-free manner. Our approach can also be applied to text-guided image generation, where we can run stable diffusion in 4-bit weights with high generation quality for the first time.

Editing real images using a pre-trained text-to-image (T2I) diffusion/flow model often involves inverting the image into its corresponding noise map. However, inversion by itself is typically insufficient for obtaining satisfactory results, and therefore many methods additionally intervene in the sampling process. Such methods achieve improved results but are not seamlessly transferable between model architectures. Here, we introduce FlowEdit, a text-based editing method for pre-trained T2I flow models, which is inversion-free, optimization-free and model agnostic. Our method constructs an ODE that directly maps between the source and target distributions (corresponding to the source and target text prompts) and achieves a lower transport cost than the inversion approach. This leads to state-of-the-art results, as we illustrate with Stable Diffusion 3 and FLUX. Code and examples are available on the project's webpage.

Modeling the time-dependent evolution of electron density is essential for understanding quantum mechanical behaviors of condensed matter and enabling predictive simulations in spectroscopy, photochemistry, and ultrafast science. Yet, while machine learning methods have advanced static density prediction, modeling its spatiotemporal dynamics remains largely unexplored. In this work, we introduce a generative framework that combines a 3D convolutional autoencoder with a latent diffusion model (LDM) to learn electron density trajectories from ab-initio molecular dynamics (AIMD) simulations. Our method encodes electron densities into a compact latent space and predicts their future states by sampling from the learned conditional distribution, enabling stable long-horizon rollouts without drift or collapse. To preserve statistical fidelity, we incorporate a scaled Jensen-Shannon divergence regularization that aligns generated and reference density distributions. On AIMD trajectories of liquid lithium at 800 K, our model accurately captures both the spatial correlations and the log-normal-like statistical structure of the density. The proposed framework has the potential to accelerate the simulation of quantum dynamics and overcome key challenges faced by current spatiotemporal machine learning methods as surrogates of quantum mechanical simulators.

The diffusion model is a state-of-the-art generative model that generates an image by applying a neural network iteratively. Moreover, this generation process is regarded as an algorithm solving an ordinary differential equation or a stochastic differential equation. Based on the analysis of the truncation error of the diffusion ODE and SDE, our study proposes a training-free algorithm that generates high-quality 512 x 512 and 1024 x 1024 images in eight steps, with flexible guidance scales. To the best of my knowledge, our algorithm is the first one that samples a 1024 x 1024 resolution image in 8 steps with an FID performance comparable to that of the latest distillation model, but without additional training. Meanwhile, our algorithm can also generate a 512 x 512 image in 8 steps, and its FID performance is better than the inference result using state-of-the-art ODE solver DPM++ 2m in 20 steps. We validate our eight-step image generation algorithm using the COCO 2014, COCO 2017, and LAION datasets. And our best FID performance is 15.7, 22.35, and 17.52. While the FID performance of DPM++2m is 17.3, 23.75, and 17.33. Further, it also outperforms the state-of-the-art AMED-plugin solver, whose FID performance is 19.07, 25.50, and 18.06. We also apply the algorithm in five-step inference without additional training, for which the best FID performance in the datasets mentioned above is 19.18, 23.24, and 19.61, respectively, and is comparable to the performance of the state-of-the-art AMED Pulgin solver in eight steps, SDXL-turbo in four steps, and the state-of-the-art diffusion distillation model Flash Diffusion in five steps. We also validate our algorithm in synthesizing 1024 * 1024 images within 6 steps, whose FID performance only has a limited distance to the latest distillation algorithm. The code is in repo: https://github.com/TheLovesOfLadyPurple/Hyperparameters-are-all-you-need

Singular limits for the following indirect signalling chemotaxis system align* \left\{ array{lllllll} \partial_t n = \Delta n - \nabla \cdot (n \nabla c ) & in \Omega\times(0,\infty) , \varepsilon \partial_t c = \Delta c - c + w & in \Omega\times(0,\infty), \varepsilon \partial_t w = \tau \Delta w - w + n & in \Omega\times (0,\infty), \partial_\nu n = \partial_\nu c = \partial_\nu w = 0, &on \partial\Omega\times (0,\infty) %(n,c,w)_{t=0} = (n_0,c_0,w_0) & on \Omega, array \right. align* are investigated. More precisely, we study parabolic-elliptic simplification, or PES, varepsilonto 0^+ with fixed tau>0 up to the critical dimension N=4, and indirect-direct simplification, or IDS, (varepsilon,tau)to (0^+,0^+) up to the critical dimension N=2. These are relevant in biological situations where the signalling process is on a much faster time scale compared to the species diffusion and all interactions. Showing singular limits in critical dimensions is challenging. To deal with the PES, we carefully combine the entropy function, an Adam-type inequality, the regularisation of slow evolution, and an energy equation method to obtain strong convergence in representative spaces. For the IDS, a bootstrap argument concerning the L^p-energy function is devised, which allows us to obtain suitable uniform bounds for the singular limits. Moreover, in both scenarios, we also present the convergence rates, where the effect of the initial layer and the convergence to the critical manifold are also revealed.

Transition state (TS) structures define the critical geometries and energy barriers underlying chemical reactivity, yet their fleeting nature renders them experimentally elusive and drives the reliance on costly, high-throughput density functional theory (DFT) calculations. Here, we introduce TS-GEN, a conditional flow-matching generative model that maps samples from a simple Gaussian prior directly to transition-state saddle-point geometries in a single, deterministic pass. By embedding both reactant and product conformations as conditioning information, TS-GEN learns to transport latent noise to true TS structures via an optimal-transport path, effectively replacing the iterative optimization common in nudged-elastic band or string-method algorithms. TS-GEN delivers unprecedented accuracy, achieving a root-mean-square deviation of 0.004 mathring{A} (vs. 0.103 mathring{A} for prior state-of-the-art) and a mean barrier-height error of 1.019 {rm kcal/mol} (vs. 2.864 {rm kcal/mol}), while requiring only 0.06 {rm s} GPU time per inference. Over 87% of generated TSs meet chemical-accuracy criteria (<1.58 {rm kcal/mol} error), substantially outpacing existing methods. TS-GEN also exhibits strong transferability to out-of-distribution reactions from a larger database. By uniting sub-angstrom precision, sub-second speed, and broad applicability, TS-GEN will be highly useful for high-throughput exploration of complex reaction networks, paving the way to the exploration of novel chemical reaction mechanisms.

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.

Recent advances in fast sampling methods for diffusion models have demonstrated significant potential to accelerate generation on image modalities. We apply these methods to 3-dimensional molecular conformations by building on the recently introduced GeoLDM equivariant latent diffusion model (Xu et al., 2023). We evaluate trade-offs between speed gains and quality loss, as measured by molecular conformation structural stability. We introduce Equivariant Latent Progressive Distillation, a fast sampling algorithm that preserves geometric equivariance and accelerates generation from latent diffusion models. Our experiments demonstrate up to 7.5x gains in sampling speed with limited degradation in molecular stability. These results suggest this accelerated sampling method has strong potential for high-throughput in silico molecular conformations screening in computational biochemistry, drug discovery, and life sciences applications.

The gradual insertion method for direct calculation of the chemical potential by molecular simulation is applied in the NpT ensemble to different quadrupolar two-centre Lennard-Jones fluids at high density state points. The results agree well with Widom's test particle insertion but show at very high densities significantly smaller statistical uncertainties. The gradual insertion method, which is coupled here with preferential sampling, extends the density range where reliable information on the chemical potential can be obtained. Application details are reported.