Daily Papers

This paper introduces Diffusion Policy, a new way of generating robot behavior by representing a robot's visuomotor policy as a conditional denoising diffusion process. We benchmark Diffusion Policy across 11 different tasks from 4 different robot manipulation benchmarks and find that it consistently outperforms existing state-of-the-art robot learning methods with an average improvement of 46.9%. Diffusion Policy learns the gradient of the action-distribution score function and iteratively optimizes with respect to this gradient field during inference via a series of stochastic Langevin dynamics steps. We find that the diffusion formulation yields powerful advantages when used for robot policies, including gracefully handling multimodal action distributions, being suitable for high-dimensional action spaces, and exhibiting impressive training stability. To fully unlock the potential of diffusion models for visuomotor policy learning on physical robots, this paper presents a set of key technical contributions including the incorporation of receding horizon control, visual conditioning, and the time-series diffusion transformer. We hope this work will help motivate a new generation of policy learning techniques that are able to leverage the powerful generative modeling capabilities of diffusion models. Code, data, and training details will be publicly available.

Monocular depth estimation is a challenging task that predicts the pixel-wise depth from a single 2D image. Current methods typically model this problem as a regression or classification task. We propose DiffusionDepth, a new approach that reformulates monocular depth estimation as a denoising diffusion process. It learns an iterative denoising process to `denoise' random depth distribution into a depth map with the guidance of monocular visual conditions. The process is performed in the latent space encoded by a dedicated depth encoder and decoder. Instead of diffusing ground truth (GT) depth, the model learns to reverse the process of diffusing the refined depth of itself into random depth distribution. This self-diffusion formulation overcomes the difficulty of applying generative models to sparse GT depth scenarios. The proposed approach benefits this task by refining depth estimation step by step, which is superior for generating accurate and highly detailed depth maps. Experimental results on KITTI and NYU-Depth-V2 datasets suggest that a simple yet efficient diffusion approach could reach state-of-the-art performance in both indoor and outdoor scenarios with acceptable inference time.

Vision-Language-Action (VLA) models aim to control robots for manipulation from visual observations and natural-language instructions. However, existing hierarchical and autoregressive paradigms often introduce architectural overhead, suffer from temporal inconsistency and long-horizon error accumulation, and lack a mechanism to capture environment dynamics without extra modules. To this end, we present MMaDA-VLA, a fully native pre-trained large diffusion VLA model that unifies multi-modal understanding and generation in a single framework. Our key idea is a native discrete diffusion formulation that embeds language, images, and continuous robot controls into one discrete token space and trains a single backbone with masked token denoising to jointly generate a future goal observation and an action chunk in parallel. Iterative denoising enables global, order-free refinement, improving long-horizon consistency while grounding actions in predicted future visual outcomes without auxiliary world models. Experiments across simulation benchmarks and real-world tasks show state-of-the-art performance, achieving 98.0% average success on LIBERO and 4.78 average length on CALVIN.

Training diffusion models that work directly on lidar points at the scale of outdoor scenes is challenging due to the difficulty of generating fine-grained details from white noise over a broad field of view. The latest works addressing scene completion with diffusion models tackle this problem by reformulating the original DDPM as a local diffusion process. It contrasts with the common practice of operating at the level of objects, where vanilla DDPMs are currently used. In this work, we close the gap between these two lines of work. We identify approximations in the local diffusion formulation, show that they are not required to operate at the scene level, and that a vanilla DDPM with a well-chosen starting point is enough for completion. Finally, we demonstrate that our method, LiDPM, leads to better results in scene completion on SemanticKITTI. The project page is https://astra-vision.github.io/LiDPM .

Probabilistic human motion prediction aims to forecast multiple possible future movements from past observations. While current approaches report high diversity and realism, they often generate motions with undetected limb stretching and jitter. To address this, we introduce SkeletonDiffusion, a latent diffusion model that embeds an explicit inductive bias on the human body within its architecture and training. Our model is trained with a novel nonisotropic Gaussian diffusion formulation that aligns with the natural kinematic structure of the human skeleton. Results show that our approach outperforms conventional isotropic alternatives, consistently generating realistic predictions while avoiding artifacts such as limb distortion. Additionally, we identify a limitation in commonly used diversity metrics, which may inadvertently favor models that produce inconsistent limb lengths within the same sequence. SkeletonDiffusion sets a new benchmark on real-world datasets, outperforming various baselines across multiple evaluation metrics. Visit our project page at https://ceveloper.github.io/publications/skeletondiffusion/ .

We present SceneFactor, a diffusion-based approach for large-scale 3D scene generation that enables controllable generation and effortless editing. SceneFactor enables text-guided 3D scene synthesis through our factored diffusion formulation, leveraging latent semantic and geometric manifolds for generation of arbitrary-sized 3D scenes. While text input enables easy, controllable generation, text guidance remains imprecise for intuitive, localized editing and manipulation of the generated 3D scenes. Our factored semantic diffusion generates a proxy semantic space composed of semantic 3D boxes that enables controllable editing of generated scenes by adding, removing, changing the size of the semantic 3D proxy boxes that guides high-fidelity, consistent 3D geometric editing. Extensive experiments demonstrate that our approach enables high-fidelity 3D scene synthesis with effective controllable editing through our factored diffusion approach.

Leveraging the visual priors of pre-trained text-to-image diffusion models offers a promising solution to enhance zero-shot generalization in dense prediction tasks. However, existing methods often uncritically use the original diffusion formulation, which may not be optimal due to the fundamental differences between dense prediction and image generation. In this paper, we provide a systemic analysis of the diffusion formulation for the dense prediction, focusing on both quality and efficiency. And we find that the original parameterization type for image generation, which learns to predict noise, is harmful for dense prediction; the multi-step noising/denoising diffusion process is also unnecessary and challenging to optimize. Based on these insights, we introduce Lotus, a diffusion-based visual foundation model with a simple yet effective adaptation protocol for dense prediction. Specifically, Lotus is trained to directly predict annotations instead of noise, thereby avoiding harmful variance. We also reformulate the diffusion process into a single-step procedure, simplifying optimization and significantly boosting inference speed. Additionally, we introduce a novel tuning strategy called detail preserver, which achieves more accurate and fine-grained predictions. Without scaling up the training data or model capacity, Lotus achieves SoTA performance in zero-shot depth and normal estimation across various datasets. It also significantly enhances efficiency, being hundreds of times faster than most existing diffusion-based methods.

We propose L3DG, the first approach for generative 3D modeling of 3D Gaussians through a latent 3D Gaussian diffusion formulation. This enables effective generative 3D modeling, scaling to generation of entire room-scale scenes which can be very efficiently rendered. To enable effective synthesis of 3D Gaussians, we propose a latent diffusion formulation, operating in a compressed latent space of 3D Gaussians. This compressed latent space is learned by a vector-quantized variational autoencoder (VQ-VAE), for which we employ a sparse convolutional architecture to efficiently operate on room-scale scenes. This way, the complexity of the costly generation process via diffusion is substantially reduced, allowing higher detail on object-level generation, as well as scalability to large scenes. By leveraging the 3D Gaussian representation, the generated scenes can be rendered from arbitrary viewpoints in real-time. We demonstrate that our approach significantly improves visual quality over prior work on unconditional object-level radiance field synthesis and showcase its applicability to room-scale scene generation.

Flow matching casts sample generation as learning a continuous-time velocity field that transports noise to data. Existing flow matching networks typically predict each point's velocity independently, considering only its location and time along its flow trajectory, and ignoring neighboring points. However, this pointwise approach may overlook correlations between points along the generation trajectory that could enhance velocity predictions, thereby improving downstream generation quality. To address this, we propose Graph Flow Matching (GFM), a lightweight enhancement that decomposes the learned velocity into a reaction term -- any standard flow matching network -- and a diffusion term that aggregates neighbor information via a graph neural module. This reaction-diffusion formulation retains the scalability of deep flow models while enriching velocity predictions with local context, all at minimal additional computational cost. Operating in the latent space of a pretrained variational autoencoder, GFM consistently improves Fr\'echet Inception Distance (FID) and recall across five image generation benchmarks (LSUN Church, LSUN Bedroom, FFHQ, AFHQ-Cat, and CelebA-HQ at 256times256), demonstrating its effectiveness as a modular enhancement to existing flow matching architectures.

Generating high-dimensional visual modalities is a computationally intensive task. A common solution is progressive generation, where the outputs are synthesized in a coarse-to-fine spectral autoregressive manner. While diffusion models benefit from the coarse-to-fine nature of denoising, explicit multi-stage architectures are rarely adopted. These architectures have increased the complexity of the overall approach, introducing the need for a custom diffusion formulation, decomposition-dependent stage transitions, add-hoc samplers, or a model cascade. Our contribution, Decomposable Flow Matching (DFM), is a simple and effective framework for the progressive generation of visual media. DFM applies Flow Matching independently at each level of a user-defined multi-scale representation (such as Laplacian pyramid). As shown by our experiments, our approach improves visual quality for both images and videos, featuring superior results compared to prior multistage frameworks. On Imagenet-1k 512px, DFM achieves 35.2% improvements in FDD scores over the base architecture and 26.4% over the best-performing baseline, under the same training compute. When applied to finetuning of large models, such as FLUX, DFM shows faster convergence speed to the training distribution. Crucially, all these advantages are achieved with a single model, architectural simplicity, and minimal modifications to existing training pipelines.

Diffusion models create data from noise by inverting the forward paths of data towards noise and have emerged as a powerful generative modeling technique for high-dimensional, perceptual data such as images and videos. Rectified flow is a recent generative model formulation that connects data and noise in a straight line. Despite its better theoretical properties and conceptual simplicity, it is not yet decisively established as standard practice. In this work, we improve existing noise sampling techniques for training rectified flow models by biasing them towards perceptually relevant scales. Through a large-scale study, we demonstrate the superior performance of this approach compared to established diffusion formulations for high-resolution text-to-image synthesis. Additionally, we present a novel transformer-based architecture for text-to-image generation that uses separate weights for the two modalities and enables a bidirectional flow of information between image and text tokens, improving text comprehension, typography, and human preference ratings. We demonstrate that this architecture follows predictable scaling trends and correlates lower validation loss to improved text-to-image synthesis as measured by various metrics and human evaluations. Our largest models outperform state-of-the-art models, and we will make our experimental data, code, and model weights publicly available.

We present a unified probabilistic formulation for diffusion-based image editing, where a latent variable is edited in a task-specific manner and generally deviates from the corresponding marginal distribution induced by the original stochastic or ordinary differential equation (SDE or ODE). Instead, it defines a corresponding SDE or ODE for editing. In the formulation, we prove that the Kullback-Leibler divergence between the marginal distributions of the two SDEs gradually decreases while that for the ODEs remains as the time approaches zero, which shows the promise of SDE in image editing. Inspired by it, we provide the SDE counterparts for widely used ODE baselines in various tasks including inpainting and image-to-image translation, where SDE shows a consistent and substantial improvement. Moreover, we propose SDE-Drag -- a simple yet effective method built upon the SDE formulation for point-based content dragging. We build a challenging benchmark (termed DragBench) with open-set natural, art, and AI-generated images for evaluation. A user study on DragBench indicates that SDE-Drag significantly outperforms our ODE baseline, existing diffusion-based methods, and the renowned DragGAN. Our results demonstrate the superiority and versatility of SDE in image editing and push the boundary of diffusion-based editing methods.

Generative tasks about molecules, including but not limited to molecule generation, are crucial for drug discovery and material design, and have consistently attracted significant attention. In recent years, diffusion models have emerged as an impressive class of deep generative models, sparking extensive research and leading to numerous studies on their application to molecular generative tasks. Despite the proliferation of related work, there remains a notable lack of up-to-date and systematic surveys in this area. Particularly, due to the diversity of diffusion model formulations, molecular data modalities, and generative task types, the research landscape is challenging to navigate, hindering understanding and limiting the area's growth. To address this, this paper conducts a comprehensive survey of diffusion model-based molecular generative methods. We systematically review the research from the perspectives of methodological formulations, data modalities, and task types, offering a novel taxonomy. This survey aims to facilitate understanding and further flourishing development in this area. The relevant papers are summarized at: https://github.com/AzureLeon1/awesome-molecular-diffusion-models.

Modeling Lagrangian turbulence remains a fundamental challenge due to its multiscale, intermittent, and non-Gaussian nature. Recent advances in data-driven diffusion models have enabled the generation of realistic Lagrangian velocity trajectories that accurately reproduce statistical properties across scales and capture rare extreme events. This study investigates three key aspects of diffusion-based modeling for Lagrangian turbulence. First, we assess architectural robustness by comparing a U-Net backbone with a transformer-based alternative, finding strong consistency in generated trajectories, with only minor discrepancies at small scales. Second, leveraging a deterministic variant of diffusion model formulation, namely the deterministic denoising diffusion implicit model (DDIM), we identify structured features in the initial latent noise that align consistently with extreme acceleration events. Third, we explore accelerated generation by reducing the number of diffusion steps, and find that DDIM enables substantial speedups with minimal loss of statistical fidelity. These findings highlight the robustness of diffusion models and their potential for interpretable, scalable modeling of complex turbulent systems.

We present AROMA (Attentive Reduced Order Model with Attention), a framework designed to enhance the modeling of partial differential equations (PDEs) using local neural fields. Our flexible encoder-decoder architecture can obtain smooth latent representations of spatial physical fields from a variety of data types, including irregular-grid inputs and point clouds. This versatility eliminates the need for patching and allows efficient processing of diverse geometries. The sequential nature of our latent representation can be interpreted spatially and permits the use of a conditional transformer for modeling the temporal dynamics of PDEs. By employing a diffusion-based formulation, we achieve greater stability and enable longer rollouts compared to conventional MSE training. AROMA's superior performance in simulating 1D and 2D equations underscores the efficacy of our approach in capturing complex dynamical behaviors.

Text-to-image synthesis (T2I) has advanced remarkably with the emergence of large-scale diffusion models. In the conventional setup, the text prompt provides explicit, user-defined guidance, directing the generation process by denoising a randomly sampled Gaussian noise. In this work, we reveal that the often-overlooked noise itself encodes inherent generative tendencies, acting as a "silent prompt" that implicitly guides the output. This implicit guidance, embedded in the noise scheduler design of diffusion model formulations and their training stages, generalizes across a wide range of T2I models and backbones. Building on this insight, we introduce NoiseQuery, a novel strategy that selects optimal initial noise from a pre-built noise library to meet diverse user needs. Our approach not only enhances high-level semantic alignment with text prompts, but also allows for nuanced adjustments of low-level visual attributes, such as texture, sharpness, shape, and color, which are typically challenging to control through text alone. Extensive experiments across various models and target attributes demonstrate the strong performance and zero-shot transferability of our approach, requiring no additional optimization.

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

Text-to-audio systems, while increasingly performant, are slow at inference time, thus making their latency unpractical for many creative applications. We present Adversarial Relativistic-Contrastive (ARC) post-training, the first adversarial acceleration algorithm for diffusion/flow models not based on distillation. While past adversarial post-training methods have struggled to compare against their expensive distillation counterparts, ARC post-training is a simple procedure that (1) extends a recent relativistic adversarial formulation to diffusion/flow post-training and (2) combines it with a novel contrastive discriminator objective to encourage better prompt adherence. We pair ARC post-training with a number optimizations to Stable Audio Open and build a model capable of generating approx12s of 44.1kHz stereo audio in approx75ms on an H100, and approx7s on a mobile edge-device, the fastest text-to-audio model to our knowledge.

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.

Online reinforcement learning (RL) has been central to post-training language models, but its extension to diffusion models remains challenging due to intractable likelihoods. Recent works discretize the reverse sampling process to enable GRPO-style training, yet they inherit fundamental drawbacks, including solver restrictions, forward-reverse inconsistency, and complicated integration with classifier-free guidance (CFG). We introduce Diffusion Negative-aware FineTuning (DiffusionNFT), a new online RL paradigm that optimizes diffusion models directly on the forward process via flow matching. DiffusionNFT contrasts positive and negative generations to define an implicit policy improvement direction, naturally incorporating reinforcement signals into the supervised learning objective. This formulation enables training with arbitrary black-box solvers, eliminates the need for likelihood estimation, and requires only clean images rather than sampling trajectories for policy optimization. DiffusionNFT is up to 25times more efficient than FlowGRPO in head-to-head comparisons, while being CFG-free. For instance, DiffusionNFT improves the GenEval score from 0.24 to 0.98 within 1k steps, while FlowGRPO achieves 0.95 with over 5k steps and additional CFG employment. By leveraging multiple reward models, DiffusionNFT significantly boosts the performance of SD3.5-Medium in every benchmark tested.

We introduce Generalized Discrete Diffusion from Snapshots (GDDS), a unified framework for discrete diffusion modeling that supports arbitrary noising processes over large discrete state spaces. Our formulation encompasses all existing discrete diffusion approaches, while allowing significantly greater flexibility in the choice of corruption dynamics. The forward noising process relies on uniformization and enables fast arbitrary corruption. For the reverse process, we derive a simple evidence lower bound (ELBO) based on snapshot latents, instead of the entire noising path, that allows efficient training of standard generative modeling architectures with clear probabilistic interpretation. Our experiments on large-vocabulary discrete generation tasks suggest that the proposed framework outperforms existing discrete diffusion methods in terms of training efficiency and generation quality, and beats autoregressive models for the first time at this scale. We provide the code along with a blog post on the project page : https://oussamazekri.fr/gdds{https://oussamazekri.fr/gdds}.

We present SketchDNN, a generative model for synthesizing CAD sketches that jointly models both continuous parameters and discrete class labels through a unified continuous-discrete diffusion process. Our core innovation is Gaussian-Softmax diffusion, where logits perturbed with Gaussian noise are projected onto the probability simplex via a softmax transformation, facilitating blended class labels for discrete variables. This formulation addresses 2 key challenges, namely, the heterogeneity of primitive parameterizations and the permutation invariance of primitives in CAD sketches. Our approach significantly improves generation quality, reducing Fréchet Inception Distance (FID) from 16.04 to 7.80 and negative log-likelihood (NLL) from 84.8 to 81.33, establishing a new state-of-the-art in CAD sketch generation on the SketchGraphs dataset.

Training diffusion models for audiovisual sequences allows for a range of generation tasks by learning conditional distributions of various input-output combinations of the two modalities. Nevertheless, this strategy often requires training a separate model for each task which is expensive. Here, we propose a novel training approach to effectively learn arbitrary conditional distributions in the audiovisual space.Our key contribution lies in how we parameterize the diffusion timestep in the forward diffusion process. Instead of the standard fixed diffusion timestep, we propose applying variable diffusion timesteps across the temporal dimension and across modalities of the inputs. This formulation offers flexibility to introduce variable noise levels for various portions of the input, hence the term mixture of noise levels. We propose a transformer-based audiovisual latent diffusion model and show that it can be trained in a task-agnostic fashion using our approach to enable a variety of audiovisual generation tasks at inference time. Experiments demonstrate the versatility of our method in tackling cross-modal and multimodal interpolation tasks in the audiovisual space. Notably, our proposed approach surpasses baselines in generating temporally and perceptually consistent samples conditioned on the input. Project page: avdit2024.github.io

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

Denoising diffusion models have recently shown impressive results in generative tasks. By learning powerful priors from huge collections of training images, such models are able to gradually modify complete noise to a clean natural image via a sequence of small denoising steps, seemingly making them well-suited for single image denoising. However, effectively applying denoising diffusion models to removal of realistic noise is more challenging than it may seem, since their formulation is based on additive white Gaussian noise, unlike noise in real-world images. In this work, we present SVNR, a novel formulation of denoising diffusion that assumes a more realistic, spatially-variant noise model. SVNR enables using the noisy input image as the starting point for the denoising diffusion process, in addition to conditioning the process on it. To this end, we adapt the diffusion process to allow each pixel to have its own time embedding, and propose training and inference schemes that support spatially-varying time maps. Our formulation also accounts for the correlation that exists between the condition image and the samples along the modified diffusion process. In our experiments we demonstrate the advantages of our approach over a strong diffusion model baseline, as well as over a state-of-the-art single image denoising method.

Joint image-feature generative modeling has recently emerged as an effective strategy for improving diffusion training by coupling low-level VAE latents with high-level semantic features extracted from pre-trained visual encoders. However, existing approaches rely on a fixed representation space, constructed independently of the generative objective and kept unchanged during training. We argue that the representation space guiding diffusion should itself adapt to the generative task. To this end, we propose Coevolving Representation Diffusion (CoReDi), a framework in which the semantic representation space evolves during training by learning a lightweight linear projection jointly with the diffusion model. While naively optimizing this projection leads to degenerate solutions, we show that stable coevolution can be achieved through a combination of stop-gradient targets, normalization, and targeted regularization that prevents feature collapse. This formulation enables the semantic space to progressively specialize to the needs of image synthesis, improving its complementarity with image latents. We apply CoReDi to both VAE latent diffusion and pixel-space diffusion, demonstrating that adaptive semantic representations improve generative modeling across both settings. Experiments show that CoReDi achieves faster convergence and higher sample quality compared to joint diffusion models operating in fixed representation spaces.

In this paper we propose a novel generative approach, DiffRoll, to tackle automatic music transcription (AMT). Instead of treating AMT as a discriminative task in which the model is trained to convert spectrograms into piano rolls, we think of it as a conditional generative task where we train our model to generate realistic looking piano rolls from pure Gaussian noise conditioned on spectrograms. This new AMT formulation enables DiffRoll to transcribe, generate and even inpaint music. Due to the classifier-free nature, DiffRoll is also able to be trained on unpaired datasets where only piano rolls are available. Our experiments show that DiffRoll outperforms its discriminative counterpart by 19 percentage points (ppt.) and our ablation studies also indicate that it outperforms similar existing methods by 4.8 ppt. Source code and demonstration are available https://sony.github.io/DiffRoll/.

Diffusion-based neural solvers have shown strong promise for combinatorial optimization (CO), but existing methods typically rely on supervised training with large collections of near-optimal solutions. In this work, we extend adjoint-based trajectory optimization methods to discrete combinatorial domains. We formulate diffusion-based CO as a stochastic control problem over Continuous-Time Markov Chains and introduce discrete adjoint dynamics for propagating optimization signals through discrete generative trajectories. Building on this formulation, we propose Combinatorial Adjoint Matching (CAM), an unsupervised training framework for discrete diffusion solvers with structured and low-variance trajectory-level optimization signals. Empirically, CAM consistently outperforms existing unsupervised diffusion baselines and achieves performance competitive with strong supervised diffusion solvers and even traditional solvers across diverse combinatorial optimization problems. Our code is available at https://github.com/Shengyu-Feng/CAM.

The rapid development of diffusion models (DMs) has significantly advanced image and video applications, making "what you want is what you see" a reality. Among these, video editing has gained substantial attention and seen a swift rise in research activity, necessitating a comprehensive and systematic review of the existing literature. This paper reviews diffusion model-based video editing techniques, including theoretical foundations and practical applications. We begin by overviewing the mathematical formulation and image domain's key methods. Subsequently, we categorize video editing approaches by the inherent connections of their core technologies, depicting evolutionary trajectory. This paper also dives into novel applications, including point-based editing and pose-guided human video editing. Additionally, we present a comprehensive comparison using our newly introduced V2VBench. Building on the progress achieved to date, the paper concludes with ongoing challenges and potential directions for future research.

Diffusion Probabilistic Models (DPMs) have recently been employed for image deblurring, formulated as an image-conditioned generation process that maps Gaussian noise to the high-quality image, conditioned on the blurry input. Image-conditioned DPMs (icDPMs) have shown more realistic results than regression-based methods when trained on pairwise in-domain data. However, their robustness in restoring images is unclear when presented with out-of-domain images as they do not impose specific degradation models or intermediate constraints. To this end, we introduce a simple yet effective multiscale structure guidance as an implicit bias that informs the icDPM about the coarse structure of the sharp image at the intermediate layers. This guided formulation leads to a significant improvement of the deblurring results, particularly on unseen domain. The guidance is extracted from the latent space of a regression network trained to predict the clean-sharp target at multiple lower resolutions, thus maintaining the most salient sharp structures. With both the blurry input and multiscale guidance, the icDPM model can better understand the blur and recover the clean image. We evaluate a single-dataset trained model on diverse datasets and demonstrate more robust deblurring results with fewer artifacts on unseen data. Our method outperforms existing baselines, achieving state-of-the-art perceptual quality while keeping competitive distortion metrics.

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 probabilistic models (DPMs) have exhibited excellent performance for high-fidelity image generation while suffering from inefficient sampling. Recent works accelerate the sampling procedure by proposing fast ODE solvers that leverage the specific ODE form of DPMs. However, they highly rely on specific parameterization during inference (such as noise/data prediction), which might not be the optimal choice. In this work, we propose a novel formulation towards the optimal parameterization during sampling that minimizes the first-order discretization error of the ODE solution. Based on such formulation, we propose DPM-Solver-v3, a new fast ODE solver for DPMs by introducing several coefficients efficiently computed on the pretrained model, which we call empirical model statistics. We further incorporate multistep methods and a predictor-corrector framework, and propose some techniques for improving sample quality at small numbers of function evaluations (NFE) or large guidance scales. Experiments show that DPM-Solver-v3 achieves consistently better or comparable performance in both unconditional and conditional sampling with both pixel-space and latent-space DPMs, especially in 5sim10 NFEs. We achieve FIDs of 12.21 (5 NFE), 2.51 (10 NFE) on unconditional CIFAR10, and MSE of 0.55 (5 NFE, 7.5 guidance scale) on Stable Diffusion, bringing a speed-up of 15\%sim30\% compared to previous state-of-the-art training-free methods. Code is available at https://github.com/thu-ml/DPM-Solver-v3.

Camera pose estimation is a long-standing computer vision problem that to date often relies on classical methods, such as handcrafted keypoint matching, RANSAC and bundle adjustment. In this paper, we propose to formulate the Structure from Motion (SfM) problem inside a probabilistic diffusion framework, modelling the conditional distribution of camera poses given input images. This novel view of an old problem has several advantages. (i) The nature of the diffusion framework mirrors the iterative procedure of bundle adjustment. (ii) The formulation allows a seamless integration of geometric constraints from epipolar geometry. (iii) It excels in typically difficult scenarios such as sparse views with wide baselines. (iv) The method can predict intrinsics and extrinsics for an arbitrary amount of images. We demonstrate that our method PoseDiffusion significantly improves over the classic SfM pipelines and the learned approaches on two real-world datasets. Finally, it is observed that our method can generalize across datasets without further training. Project page: https://posediffusion.github.io/

The gradual nature of a diffusion process that synthesizes samples in small increments constitutes a key ingredient of Denoising Diffusion Probabilistic Models (DDPM), which have presented unprecedented quality in image synthesis and been recently explored in the motion domain. In this work, we propose to adapt the gradual diffusion concept (operating along a diffusion time-axis) into the temporal-axis of the motion sequence. Our key idea is to extend the DDPM framework to support temporally varying denoising, thereby entangling the two axes. Using our special formulation, we iteratively denoise a motion buffer that contains a set of increasingly-noised poses, which auto-regressively produces an arbitrarily long stream of frames. With a stationary diffusion time-axis, in each diffusion step we increment only the temporal-axis of the motion such that the framework produces a new, clean frame which is removed from the beginning of the buffer, followed by a newly drawn noise vector that is appended to it. This new mechanism paves the way towards a new framework for long-term motion synthesis with applications to character animation and other domains.

Masked diffusion models (MDMs) have shown promise in language modeling, yet their scalability and effectiveness in core language tasks, such as text generation and language understanding, remain underexplored. This paper establishes the first scaling law for MDMs, demonstrating a scaling rate comparable to autoregressive models (ARMs) and a relatively small compute gap. Motivated by their scalability, we train a family of MDMs with up to 1.1 billion (B) parameters to systematically evaluate their performance against ARMs of comparable or larger sizes. Fully leveraging the probabilistic formulation of MDMs, we propose a simple yet effective unsupervised classifier-free guidance that effectively exploits large-scale unpaired data, boosting performance for conditional inference. In language understanding, the 1.1B MDM outperforms the 1.1B TinyLlama model trained on the same data across four of eight zero-shot benchmarks. Notably, it achieves competitive math reasoning ability with the 7B Llama-2 model on the GSM8K dataset. In text generation, MDMs with 16 times more pre-training time offer a flexible trade-off against ARMs with the accelerated sampling technique KV-Cache: MDMs match ARMs in performance while being 1.4 times faster during sampling. Moreover, MDMs address challenging tasks for ARMs by effectively handling bidirectional reasoning and adapting to temporal shifts in data. Notably, a 1.1B MDM breaks the reverse curse encountered by much larger ARMs with significantly more data and computation, such as 13B Llama-2 and 175B GPT-3. Our code is available at https://github.com/ML-GSAI/SMDM.

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

Diffusion-based generative models have achieved remarkable success in image generation. Their guidance formulation allows an external model to plug-and-play control the generation process for various tasks without finetuning the diffusion model. However, the direct use of publicly available off-the-shelf models for guidance fails due to their poor performance on noisy inputs. For that, the existing practice is to fine-tune the guidance models with labeled data corrupted with noises. In this paper, we argue that this practice has limitations in two aspects: (1) performing on inputs with extremely various noises is too hard for a single guidance model; (2) collecting labeled datasets hinders scaling up for various tasks. To tackle the limitations, we propose a novel strategy that leverages multiple experts where each expert is specialized in a particular noise range and guides the reverse process of the diffusion at its corresponding timesteps. However, as it is infeasible to manage multiple networks and utilize labeled data, we present a practical guidance framework termed Practical Plug-And-Play (PPAP), which leverages parameter-efficient fine-tuning and data-free knowledge transfer. We exhaustively conduct ImageNet class conditional generation experiments to show that our method can successfully guide diffusion with small trainable parameters and no labeled data. Finally, we show that image classifiers, depth estimators, and semantic segmentation models can guide publicly available GLIDE through our framework in a plug-and-play manner. Our code is available at https://github.com/riiid/PPAP.

Reinforcement learning fine-tuning has become the dominant approach for aligning diffusion models with human preferences. However, assessing images is intrinsically a multi-dimensional task, and multiple evaluation criteria need to be optimized simultaneously. Existing practice deal with multiple rewards by training one specialist model per reward, optimizing a weighted-sum reward R(x)=sum_k w_k R_k(x), or sequentially fine-tuning with a hand-crafted stage schedule. These approaches either fail to produce a unified model that can be jointly trained on all rewards or necessitates heavy manually tuned sequential training. We find that the failure stems from using a naive weighted-sum reward aggregation. This approach suffers from a sample-level mismatch because most rollouts are specialist samples, highly informative for certain reward dimensions but irrelevant for others; consequently, weighted summation dilutes their supervision. To address this issue, we propose MARBLE (Multi-Aspect Reward BaLancE), a gradient-space optimization framework that maintains independent advantage estimators for each reward, computes per-reward policy gradients, and harmonizes them into a single update direction without manually-tuned reward weighting, by solving a Quadratic Programming problem. We further propose an amortized formulation that exploits the affine structure of the loss used in DiffusionNFT, to reduce the per-step cost from K+1 backward passes to near single-reward baseline cost, together with EMA smoothing on the balancing coefficients to stabilize updates against transient single-batch fluctuations. On SD3.5 Medium with five rewards, MARBLE improves all five reward dimensions simultaneously, turns the worst-aligned reward's gradient cosine from negative under weighted summation in 80% of mini-batches to consistently positive, and runs at 0.97X the training speed of baseline training.

Step distillation has become a leading technique for accelerating diffusion models, among which Distribution Matching Distillation (DMD) and Consistency Distillation are two representative paradigms. While consistency methods enforce self-consistency along the full PF-ODE trajectory to steer it toward the clean data manifold, vanilla DMD relies on sparse supervision at a few predefined discrete timesteps. This restricted discrete-time formulation and mode-seeking nature of the reverse KL divergence tends to exhibit visual artifacts and over-smoothed outputs, often necessitating complex auxiliary modules -- such as GANs or reward models -- to restore visual fidelity. In this work, we introduce Continuous-Time Distribution Matching (CDM), migrating the DMD framework from discrete anchoring to continuous optimization for the first time. CDM achieves this through two continuous-time designs. First, we replace the fixed discrete schedule with a dynamic continuous schedule of random length, so that distribution matching is enforced at arbitrary points along sampling trajectories rather than only at a few fixed anchors. Second, we propose a continuous-time alignment objective that performs active off-trajectory matching on latents extrapolated via the student's velocity field, improving generalization and preserving fine visual details. Extensive experiments on different architectures, including SD3-Medium and Longcat-Image, demonstrate that CDM provides highly competitive visual fidelity for few-step image generation without relying on complex auxiliary objectives. Code is available at https://github.com/byliutao/cdm.

We characterize the pre-softmax attention matrix QK^top in transformers as an associative memory matrix encoding pairwise associations between input features. By decomposing this matrix into its symmetric and skew-symmetric parts, we interpret the symmetric component as governing the structure of the energy landscape, and the skew-symmetric component as driving circulation on that landscape. Leveraging the energy formulation induced by the symmetric component, we derive Hopfield-style stability measures that quantify the stability of retrieved features. We observe meaningful correlations between Hopfield-style stability measures and the fidelity-diversity trade-offs in generation. Finally, we propose a controllable knob to modulate this trade-off by modifying the circulation of the underlying dynamics. Code is available at our GitHub (https://github.com/hyeon-cho/Attention-Symmetric-Decomposition).

A diffusion probabilistic model (DPM), which constructs a forward diffusion process by gradually adding noise to data points and learns the reverse denoising process to generate new samples, has been shown to handle complex data distribution. Despite its recent success in image synthesis, applying DPMs to video generation is still challenging due to high-dimensional data spaces. Previous methods usually adopt a standard diffusion process, where frames in the same video clip are destroyed with independent noises, ignoring the content redundancy and temporal correlation. This work presents a decomposed diffusion process via resolving the per-frame noise into a base noise that is shared among all frames and a residual noise that varies along the time axis. The denoising pipeline employs two jointly-learned networks to match the noise decomposition accordingly. Experiments on various datasets confirm that our approach, termed as VideoFusion, surpasses both GAN-based and diffusion-based alternatives in high-quality video generation. We further show that our decomposed formulation can benefit from pre-trained image diffusion models and well-support text-conditioned video creation.

Video summarization is a task of shortening a video by choosing a subset of frames while preserving its essential moments. Despite the innate subjectivity of the task, previous works have deterministically regressed to an averaged frame score over multiple raters, ignoring the inherent subjectivity of what constitutes a good summary. We propose a novel problem formulation by framing video summarization as a conditional generation task, allowing a model to learn the distribution of good summaries and to generate multiple plausible summaries that better reflect varying human perspectives. Adopting diffusion models for the first time in video summarization, our proposed method, SummDiff, dynamically adapts to visual contexts and generates multiple candidate summaries conditioned on the input video. Extensive experiments demonstrate that SummDiff not only achieves the state-of-the-art performance on various benchmarks but also produces summaries that closely align with individual annotator preferences. Moreover, we provide a deeper insight with novel metrics from an analysis of the knapsack, which is an important last step of generating summaries but has been overlooked in evaluation.

Reconstructing 3D clothed humans from monocular images and videos is a fundamental problem with applications in virtual try-on, avatar creation, and mixed reality. Despite significant progress in human body recovery, accurately reconstructing garment geometry, particularly for loose-fitting clothing, remains an open challenge. We propose a unified framework for high-fidelity 3D garment reconstruction from both single images and video sequences. Our approach combines Implicit Sewing Patterns (ISP) with a generative diffusion model to learn expressive garment shape priors in 2D UV space. Leveraging these priors, we introduce a mapping model that establishes correspondences between image pixels, UV pattern coordinates, and 3D geometry, enabling accurate and detailed garment reconstruction from single images. We further extend this formulation to dynamic reconstruction by introducing a spatio-temporal diffusion scheme with test-time guidance to enforce long-range temporal consistency. We also develop analytic projection-based constraints that preserve image-aligned geometry in visible regions while enforcing coherent completion in occluded areas over time. Although trained exclusively on synthetically simulated cloth data, our method generalizes well to real-world imagery and consistently outperforms existing approaches on both tight- and loose-fitting garments. The reconstructed garments preserve fine geometric detail while exhibiting realistic dynamic motion, supporting downstream applications such as texture editing, garment retargeting, and animation.

Recent advancements in timestep-distilled diffusion models have enabled high-quality image generation that rivals non-distilled multi-step models, but with significantly fewer inference steps. While such models are attractive for applications due to the low inference cost and latency, fine-tuning them with a naive diffusion objective would result in degraded and blurry outputs. An intuitive alternative is to repeat the diffusion distillation process with a fine-tuned teacher model, which produces good results but is cumbersome and computationally intensive; the distillation training usually requires magnitude higher of training compute compared to fine-tuning for specific image styles. In this paper, we present an algorithm named pairwise sample optimization (PSO), which enables the direct fine-tuning of an arbitrary timestep-distilled diffusion model. PSO introduces additional reference images sampled from the current time-step distilled model, and increases the relative likelihood margin between the training images and reference images. This enables the model to retain its few-step generation ability, while allowing for fine-tuning of its output distribution. We also demonstrate that PSO is a generalized formulation which can be flexibly extended to both offline-sampled and online-sampled pairwise data, covering various popular objectives for diffusion model preference optimization. We evaluate PSO in both preference optimization and other fine-tuning tasks, including style transfer and concept customization. We show that PSO can directly adapt distilled models to human-preferred generation with both offline and online-generated pairwise preference image data. PSO also demonstrates effectiveness in style transfer and concept customization by directly tuning timestep-distilled diffusion models.

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

Denoising diffusion models have shown great promise in human motion synthesis conditioned on natural language descriptions. However, integrating spatial constraints, such as pre-defined motion trajectories and obstacles, remains a challenge despite being essential for bridging the gap between isolated human motion and its surrounding environment. To address this issue, we propose Guided Motion Diffusion (GMD), a method that incorporates spatial constraints into the motion generation process. Specifically, we propose an effective feature projection scheme that manipulates motion representation to enhance the coherency between spatial information and local poses. Together with a new imputation formulation, the generated motion can reliably conform to spatial constraints such as global motion trajectories. Furthermore, given sparse spatial constraints (e.g. sparse keyframes), we introduce a new dense guidance approach to turn a sparse signal, which is susceptible to being ignored during the reverse steps, into denser signals to guide the generated motion to the given constraints. Our extensive experiments justify the development of GMD, which achieves a significant improvement over state-of-the-art methods in text-based motion generation while allowing control of the synthesized motions with spatial constraints.

We propose a new formulation of temporal action detection (TAD) with denoising diffusion, DiffTAD in short. Taking as input random temporal proposals, it can yield action proposals accurately given an untrimmed long video. This presents a generative modeling perspective, against previous discriminative learning manners. This capability is achieved by first diffusing the ground-truth proposals to random ones (i.e., the forward/noising process) and then learning to reverse the noising process (i.e., the backward/denoising process). Concretely, we establish the denoising process in the Transformer decoder (e.g., DETR) by introducing a temporal location query design with faster convergence in training. We further propose a cross-step selective conditioning algorithm for inference acceleration. Extensive evaluations on ActivityNet and THUMOS show that our DiffTAD achieves top performance compared to previous art alternatives. The code will be made available at https://github.com/sauradip/DiffusionTAD.

This work studies discrete diffusion probabilistic models with applications to natural language generation. We derive an alternative yet equivalent formulation of the sampling from discrete diffusion processes and leverage this insight to develop a family of reparameterized discrete diffusion models. The derived generic framework is highly flexible, offers a fresh perspective of the generation process in discrete diffusion models, and features more effective training and decoding techniques. We conduct extensive experiments to evaluate the text generation capability of our model, demonstrating significant improvements over existing diffusion models.

Solving ill-posed inverse problems requires careful formulation of prior beliefs over the signals of interest and an accurate description of their manifestation into noisy measurements. Handcrafted signal priors based on e.g. sparsity are increasingly replaced by data-driven deep generative models, and several groups have recently shown that state-of-the-art score-based diffusion models yield particularly strong performance and flexibility. In this paper, we show that the powerful paradigm of posterior sampling with diffusion models can be extended to include rich, structured, noise models. To that end, we propose a joint conditional reverse diffusion process with learned scores for the noise and signal-generating distribution. We demonstrate strong performance gains across various inverse problems with structured noise, outperforming competitive baselines that use normalizing flows and adversarial networks. This opens up new opportunities and relevant practical applications of diffusion modeling for inverse problems in the context of non-Gaussian measurement models.

Diffusion generative models have recently become a powerful technique for creating and modifying high-quality, coherent video content. This survey provides a comprehensive overview of the critical components of diffusion models for video generation, including their applications, architectural design, and temporal dynamics modeling. The paper begins by discussing the core principles and mathematical formulations, then explores various architectural choices and methods for maintaining temporal consistency. A taxonomy of applications is presented, categorizing models based on input modalities such as text prompts, images, videos, and audio signals. Advancements in text-to-video generation are discussed to illustrate the state-of-the-art capabilities and limitations of current approaches. Additionally, the survey summarizes recent developments in training and evaluation practices, including the use of diverse video and image datasets and the adoption of various evaluation metrics to assess model performance. The survey concludes with an examination of ongoing challenges, such as generating longer videos and managing computational costs, and offers insights into potential future directions for the field. By consolidating the latest research and developments, this survey aims to serve as a valuable resource for researchers and practitioners working with video diffusion models. Website: https://github.com/ndrwmlnk/Awesome-Video-Diffusion-Models

Dense 3D tracking from monocular video is fundamental to dynamic scene understanding. While recent 3D foundation models provide reliable per-frame geometry, recovering object motion in this geometry remains challenging and benefits from strong motion priors learned from real-world videos. Existing 3D trackers either follow iterative paradigms trained from scratch on synthetic data or fine-tune 3D reconstruction models learned from static multi-view images, both lacking real-world motion priors. Pre-trained video diffusion transformers (video DiTs) offer rich spatio-temporal priors from internet-scale videos, making them a promising foundation for 3D tracking. However, their frame-anchored formulation, which generates each frame's content, is fundamentally mismatched with reference-anchored dense 3D tracking, which must follow the same physical points from a reference frame across time. We present TrackCraft3R, the first method to repurpose a video DiT as a feed-forward dense 3D tracker. Given a monocular video and its frame-anchored reconstruction pointmap, TrackCraft3R predicts a reference-anchored tracking pointmap that follows every pixel of the first frame across time in a single forward pass, along with its visibility. We achieve this through two designs: (i) a dual-latent representation that uses per-frame geometry latents and reference-anchored track latents as dense queries, and (ii) temporal RoPE alignment, which specifies the target timestamp of each track latent. Together, these designs convert the per-frame generative paradigm of video DiTs into a reference-anchored tracking formulation with LoRA fine-tuning. TrackCraft3R achieves state-of-the-art performance on standard sparse and dense 3D tracking benchmarks, while running 1.3x faster and using 4.6x less peak memory than the strongest prior method. We further demonstrate robustness to large motions and long videos.

Group Relative Policy Optimization (GRPO) is highly effective for post-training autoregressive (AR) language models, yet its direct application to diffusion large language models (dLLMs) often triggers reward collapse. We identify two sources of incompatibility. First, GRPO relies on importance ratios defined by sequence probabilities, which are intractable in dLLMs and must be estimated (e.g., via ELBO-based or mean-field likelihood proxies), yielding inherently noisy ratios. Second, standard GRPO's formulation is not designed for estimated ratios: its conditional clipping can be anomalously bypassed by model-agnostic estimation noise, producing gradient spikes, while its fixed group-size normalization amplifies gradient-magnitude fluctuations under high-variance ratio estimates. We show these effects form a self-reinforcing instability loop that drives policy drift and further increases ratio variance. To break this loop, we propose StableDRL, a reformulation of GRPO tailored for dLLMs that uses (i) unconditional clipping to suppress outlier-induced spikes and (ii) self-normalization to constrain updates within the convex hull of per-sample gradients. We further extend StableDRL to block-wise diffusion models via a staircase attention mechanism.

Adaptation methods have been a workhorse for unlocking the transformative power of pre-trained diffusion models in diverse applications. Existing approaches often abstract adaptation objectives as a reward function and steer diffusion models to generate high-reward samples. However, these approaches can incur high computational overhead due to additional training, or rely on stringent assumptions on the reward such as differentiability. Moreover, despite their empirical success, theoretical justification and guarantees are seldom established. In this paper, we propose DOIT (Doob-Oriented Inference-time Transformation), a training-free and computationally efficient adaptation method that applies to generic, non-differentiable rewards. The key framework underlying our method is a measure transport formulation that seeks to transport the pre-trained generative distribution to a high-reward target distribution. We leverage Doob's h-transform to realize this transport, which induces a dynamic correction to the diffusion sampling process and enables efficient simulation-based computation without modifying the pre-trained model. Theoretically, we establish a high probability convergence guarantee to the target high-reward distribution via characterizing the approximation error in the dynamic Doob's correction. Empirically, on D4RL offline RL benchmarks, our method consistently outperforms state-of-the-art baselines while preserving sampling efficiency.

Modern deep learning methods typically treat image sequences as large tensors of sequentially stacked frames. However, is this straightforward representation ideal given the current state-of-the-art (SoTA)? In this work, we address this question in the context of generative models and aim to devise a more effective way of modeling image sequence data. Observing the inefficiencies and bottlenecks of current SoTA image sequence generation methods, we showcase that rather than working with large tensors, we can improve the generation process by factorizing it into first generating the coarse sequence at low resolution and then refining the individual frames at high resolution. We train a generative model solely on grid images comprising subsampled frames. Yet, we learn to generate image sequences, using the strong self-attention mechanism of the Diffusion Transformer (DiT) to capture correlations between frames. In effect, our formulation extends a 2D image generator to operate as a low-resolution 3D image-sequence generator without introducing any architectural modifications. Subsequently, we super-resolve each frame individually to add the sequence-independent high-resolution details. This approach offers several advantages and can overcome key limitations of the SoTA in this domain. Compared to existing image sequence generation models, our method achieves superior synthesis quality and improved coherence across sequences. It also delivers high-fidelity generation of arbitrary-length sequences and increased efficiency in inference time and training data usage. Furthermore, our straightforward formulation enables our method to generalize effectively across diverse data domains, which typically require additional priors and supervision to model in a generative context. Our method consistently outperforms SoTA in quality and inference speed (at least twice-as-fast) across datasets.

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

Recent text-to-image generative models have demonstrated an unparalleled ability to generate diverse and creative imagery guided by a target text prompt. While revolutionary, current state-of-the-art diffusion models may still fail in generating images that fully convey the semantics in the given text prompt. We analyze the publicly available Stable Diffusion model and assess the existence of catastrophic neglect, where the model fails to generate one or more of the subjects from the input prompt. Moreover, we find that in some cases the model also fails to correctly bind attributes (e.g., colors) to their corresponding subjects. To help mitigate these failure cases, we introduce the concept of Generative Semantic Nursing (GSN), where we seek to intervene in the generative process on the fly during inference time to improve the faithfulness of the generated images. Using an attention-based formulation of GSN, dubbed Attend-and-Excite, we guide the model to refine the cross-attention units to attend to all subject tokens in the text prompt and strengthen - or excite - their activations, encouraging the model to generate all subjects described in the text prompt. We compare our approach to alternative approaches and demonstrate that it conveys the desired concepts more faithfully across a range of text prompts.

Diffusion language models enable any-order generation and bidirectional conditioning, offering appealing flexibility for tasks such as infilling, rewriting, and self-correction. However, their formulation-predicting one part of a sequence from another within a single-step dependency-limits modeling depth and often yields lower sample quality and stability than autoregressive (AR) models. To address this, we revisit autoregressive modeling as a foundation and reformulate diffusion-style training into a structured multi-group prediction process. We propose Any-order Any-subset Autoregressive modeling (A3), a generalized framework that extends the standard AR factorization to arbitrary token groups and generation orders. A3 preserves the probabilistic rigor and multi-layer dependency modeling of AR while inheriting diffusion models' flexibility for parallel and bidirectional generation. We implement A3 through a two-stream attention architecture and a progressive adaptation strategy that transitions pretrained AR models toward any-order prediction. Experiments on question answering, commonsense reasoning, and story infilling demonstrate that A3 outperforms diffusion-based models while maintaining flexible decoding. This work offers a unified approach for a flexible, efficient, and novel language modeling paradigm.

Recent advancements in diffusion models have revolutionized generative modeling. However, the impressive and vivid outputs they produce often come at the cost of significant model scaling and increased computational demands. Consequently, building personalized diffusion models based on off-the-shelf models has emerged as an appealing alternative. In this paper, we introduce a novel perspective on conditional generation for transferring a pre-trained model. From this viewpoint, we propose *Domain Guidance*, a straightforward transfer approach that leverages pre-trained knowledge to guide the sampling process toward the target domain. Domain Guidance shares a formulation similar to advanced classifier-free guidance, facilitating better domain alignment and higher-quality generations. We provide both empirical and theoretical analyses of the mechanisms behind Domain Guidance. Our experimental results demonstrate its substantial effectiveness across various transfer benchmarks, achieving over a 19.6% improvement in FID and a 23.4% improvement in FD_DINOv2 compared to standard fine-tuning. Notably, existing fine-tuned models can seamlessly integrate Domain Guidance to leverage these benefits, without additional training.

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/

Diffusion inversion is the problem of taking an image and a text prompt that describes it and finding a noise latent that would generate the image. Most current inversion techniques operate by approximately solving an implicit equation and may converge slowly or yield poor reconstructed images. Here, we formulate the problem as finding the roots of an implicit equation and design a method to solve it efficiently. Our solution is based on Newton-Raphson (NR), a well-known technique in numerical analysis. A naive application of NR may be computationally infeasible and tends to converge to incorrect solutions. We describe an efficient regularized formulation that converges quickly to a solution that provides high-quality reconstructions. We also identify a source of inconsistency stemming from prompt conditioning during the inversion process, which significantly degrades the inversion quality. To address this, we introduce a prompt-aware adjustment of the encoding, effectively correcting this issue. Our solution, Regularized Newton-Raphson Inversion, inverts an image within 0.5 sec for latent consistency models, opening the door for interactive image editing. We further demonstrate improved results in image interpolation and generation of rare objects.

We introduce DiffRF, a novel approach for 3D radiance field synthesis based on denoising diffusion probabilistic models. While existing diffusion-based methods operate on images, latent codes, or point cloud data, we are the first to directly generate volumetric radiance fields. To this end, we propose a 3D denoising model which directly operates on an explicit voxel grid representation. However, as radiance fields generated from a set of posed images can be ambiguous and contain artifacts, obtaining ground truth radiance field samples is non-trivial. We address this challenge by pairing the denoising formulation with a rendering loss, enabling our model to learn a deviated prior that favours good image quality instead of trying to replicate fitting errors like floating artifacts. In contrast to 2D-diffusion models, our model learns multi-view consistent priors, enabling free-view synthesis and accurate shape generation. Compared to 3D GANs, our diffusion-based approach naturally enables conditional generation such as masked completion or single-view 3D synthesis at inference time.

In text-to-speech (TTS) synthesis, diffusion models have achieved promising generation quality. However, because of the pre-defined data-to-noise diffusion process, their prior distribution is restricted to a noisy representation, which provides little information of the generation target. In this work, we present a novel TTS system, Bridge-TTS, making the first attempt to substitute the noisy Gaussian prior in established diffusion-based TTS methods with a clean and deterministic one, which provides strong structural information of the target. Specifically, we leverage the latent representation obtained from text input as our prior, and build a fully tractable Schrodinger bridge between it and the ground-truth mel-spectrogram, leading to a data-to-data process. Moreover, the tractability and flexibility of our formulation allow us to empirically study the design spaces such as noise schedules, as well as to develop stochastic and deterministic samplers. Experimental results on the LJ-Speech dataset illustrate the effectiveness of our method in terms of both synthesis quality and sampling efficiency, significantly outperforming our diffusion counterpart Grad-TTS in 50-step/1000-step synthesis and strong fast TTS models in few-step scenarios. Project page: https://bridge-tts.github.io/

By decomposing the image formation process into a sequential application of denoising autoencoders, diffusion models (DMs) achieve state-of-the-art synthesis results on image data and beyond. Additionally, their formulation allows for a guiding mechanism to control the image generation process without retraining. However, since these models typically operate directly in pixel space, optimization of powerful DMs often consumes hundreds of GPU days and inference is expensive due to sequential evaluations. To enable DM training on limited computational resources while retaining their quality and flexibility, we apply them in the latent space of powerful pretrained autoencoders. In contrast to previous work, training diffusion models on such a representation allows for the first time to reach a near-optimal point between complexity reduction and detail preservation, greatly boosting visual fidelity. By introducing cross-attention layers into the model architecture, we turn diffusion models into powerful and flexible generators for general conditioning inputs such as text or bounding boxes and high-resolution synthesis becomes possible in a convolutional manner. Our latent diffusion models (LDMs) achieve a new state of the art for image inpainting and highly competitive performance on various tasks, including unconditional image generation, semantic scene synthesis, and super-resolution, while significantly reducing computational requirements compared to pixel-based DMs. Code is available at https://github.com/CompVis/latent-diffusion .

Recent advances in diffusion and flow matching models have highlighted a shift in the preferred prediction target -- moving from noise (varepsilon) and velocity (v) to direct data (x) prediction -- particularly in high-dimensional settings. However, a formal explanation of why the optimal target depends on the specific properties of the data remains elusive. In this work, we provide a theoretical framework based on a generalized prediction formulation that accommodates arbitrary output targets, of which varepsilon-, v-, and x-prediction are special cases. We derive the analytical relationship between data's geometry and the optimal prediction target, offering a rigorous justification for why x-prediction becomes superior when the ambient dimension significantly exceeds the data's intrinsic dimension. Furthermore, while our theory identifies dimensionality as the governing factor for the optimal prediction target, the intrinsic dimension of manifold-bound data is typically intractable to estimate in practice. To bridge this gap, we propose k-Diff, a framework that employs a data-driven approach to learn the optimal prediction parameter k directly from data, bypassing the need for explicit dimension estimation. Extensive experiments in both latent-space and pixel-space image generation demonstrate that k-Diff consistently outperforms fixed-target baselines across varying architectures and data scales, providing a principled and automated approach to enhancing generative performance.

Direct preference optimization (DPO) methods have shown strong potential in aligning text-to-image diffusion models with human preferences by training on paired comparisons. These methods improve training stability by avoiding the REINFORCE algorithm but still struggle with challenges such as accurately estimating image probabilities due to the non-linear nature of the sigmoid function and the limited diversity of offline datasets. In this paper, we introduce Diffusion Denoising Ranking Optimization (Diffusion-DRO), a new preference learning framework grounded in inverse reinforcement learning. Diffusion-DRO removes the dependency on a reward model by casting preference learning as a ranking problem, thereby simplifying the training objective into a denoising formulation and overcoming the non-linear estimation issues found in prior methods. Moreover, Diffusion-DRO uniquely integrates offline expert demonstrations with online policy-generated negative samples, enabling it to effectively capture human preferences while addressing the limitations of offline data. Comprehensive experiments show that Diffusion-DRO delivers improved generation quality across a range of challenging and unseen prompts, outperforming state-of-the-art baselines in both both quantitative metrics and user studies. Our source code and pre-trained models are available at https://github.com/basiclab/DiffusionDRO.

Gaussian splatting typically requires dense observations of the scene and can fail to reconstruct occluded and unobserved areas. We propose a latent diffusion model to reconstruct a complete 3D scene with Gaussian splats, including the occluded parts, from only a single image during inference. Completing the unobserved surfaces of a scene is challenging due to the ambiguity of the plausible surfaces. Conventional methods use a regression-based formulation to predict a single "mode" for occluded and out-of-frustum surfaces, leading to blurriness, implausibility, and failure to capture multiple possible explanations. Thus, they often address this problem partially, focusing either on objects isolated from the background, reconstructing only visible surfaces, or failing to extrapolate far from the input views. In contrast, we propose a generative formulation to learn a distribution of 3D representations of Gaussian splats conditioned on a single input image. To address the lack of ground-truth training data, we propose a Variational AutoReconstructor to learn a latent space only from 2D images in a self-supervised manner, over which a diffusion model is trained. Our method generates faithful reconstructions and diverse samples with the ability to complete the occluded surfaces for high-quality 360-degree renderings.

Recent progress in image generation has sparked research into controlling these models through condition signals, with various methods addressing specific challenges in conditional generation. Instead of proposing another specialized technique, we introduce a simple, unified framework to handle diverse conditional generation tasks involving a specific image-condition correlation. By learning a joint distribution over a correlated image pair (e.g. image and depth) with a diffusion model, our approach enables versatile capabilities via different inference-time sampling schemes, including controllable image generation (e.g. depth to image), estimation (e.g. image to depth), signal guidance, joint generation (image & depth), and coarse control. Previous attempts at unification often introduce significant complexity through multi-stage training, architectural modification, or increased parameter counts. In contrast, our simple formulation requires a single, computationally efficient training stage, maintains the standard model input, and adds minimal learned parameters (15% of the base model). Moreover, our model supports additional capabilities like non-spatially aligned and coarse conditioning. Extensive results show that our single model can produce comparable results with specialized methods and better results than prior unified methods. We also demonstrate that multiple models can be effectively combined for multi-signal conditional generation.

Virtual Try-on (VTON) involves generating images of a person wearing selected garments. Diffusion-based methods, in particular, can create high-quality images, but they struggle to maintain the identities of the input garments. We identified this problem stems from the specifics in the training formulation for diffusion. To address this, we propose a unique training scheme that limits the scope in which diffusion is trained. We use a control image that perfectly aligns with the target image during training. In turn, this accurately preserves garment details during inference. We demonstrate our method not only effectively conserves garment details but also allows for layering, styling, and shoe try-on. Our method runs multi-garment try-on in a single inference cycle and can support high-quality zoomed-in generations without training in higher resolutions. Finally, we show our method surpasses prior methods in accuracy and quality.

Interactive image editing allows users to modify images through visual interaction operations such as drawing, clicking, and dragging. Existing methods construct such supervision signals from videos, as they capture how objects change with various physical interactions. However, these models are usually built upon text-to-image diffusion models, so necessitate (i) massive training samples and (ii) an additional reference encoder to learn real-world dynamics and visual consistency. In this paper, we reformulate this task as an image-to-video generation problem, so that inherit powerful video diffusion priors to reduce training costs and ensure temporal consistency. Specifically, we introduce FramePainter as an efficient instantiation of this formulation. Initialized with Stable Video Diffusion, it only uses a lightweight sparse control encoder to inject editing signals. Considering the limitations of temporal attention in handling large motion between two frames, we further propose matching attention to enlarge the receptive field while encouraging dense correspondence between edited and source image tokens. We highlight the effectiveness and efficiency of FramePainter across various of editing signals: it domainantly outperforms previous state-of-the-art methods with far less training data, achieving highly seamless and coherent editing of images, \eg, automatically adjust the reflection of the cup. Moreover, FramePainter also exhibits exceptional generalization in scenarios not present in real-world videos, \eg, transform the clownfish into shark-like shape. Our code will be available at https://github.com/YBYBZhang/FramePainter.

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

Diffusion models have achieved remarkable performance in generative modeling, yet their theoretical foundations are often intricate, and the gap between mathematical formulations in papers and practical open-source implementations can be difficult to bridge. Existing tutorials primarily focus on deriving equations, offering limited guidance on how diffusion models actually operate in code. To address this, we present a concise implementation of approximately 300 lines that explains diffusion models from a code-execution perspective. Our minimal example preserves the essential components -- including forward diffusion, reverse sampling, the noise-prediction network, and the training loop -- while removing unnecessary engineering details. This technical report aims to provide researchers with a clear, implementation-first understanding of how diffusion models work in practice and how code and theory correspond. Our code and pre-trained models are available at: https://github.com/disanda/GM/tree/main/DDPM-DDIM-ClassifierFree.

Diffusion policies are conditional diffusion models that learn robot action distributions conditioned on the robot and environment state. They have recently shown to outperform both deterministic and alternative action distribution learning formulations. 3D robot policies use 3D scene feature representations aggregated from a single or multiple camera views using sensed depth. They have shown to generalize better than their 2D counterparts across camera viewpoints. We unify these two lines of work and present 3D Diffuser Actor, a neural policy equipped with a novel 3D denoising transformer that fuses information from the 3D visual scene, a language instruction and proprioception to predict the noise in noised 3D robot pose trajectories. 3D Diffuser Actor sets a new state-of-the-art on RLBench with an absolute performance gain of 18.1% over the current SOTA on a multi-view setup and an absolute gain of 13.1% on a single-view setup. On the CALVIN benchmark, it improves over the current SOTA by a 9% relative increase. It also learns to control a robot manipulator in the real world from a handful of demonstrations. Through thorough comparisons with the current SOTA policies and ablations of our model, we show 3D Diffuser Actor's design choices dramatically outperform 2D representations, regression and classification objectives, absolute attentions, and holistic non-tokenized 3D scene embeddings.

We introduce MMaDA, a novel class of multimodal diffusion foundation models designed to achieve superior performance across diverse domains such as textual reasoning, multimodal understanding, and text-to-image generation. The approach is distinguished by three key innovations: (i) MMaDA adopts a unified diffusion architecture with a shared probabilistic formulation and a modality-agnostic design, eliminating the need for modality-specific components. This architecture ensures seamless integration and processing across different data types. (ii) We implement a mixed long chain-of-thought (CoT) fine-tuning strategy that curates a unified CoT format across modalities. By aligning reasoning processes between textual and visual domains, this strategy facilitates cold-start training for the final reinforcement learning (RL) stage, thereby enhancing the model's ability to handle complex tasks from the outset. (iii) We propose UniGRPO, a unified policy-gradient-based RL algorithm specifically tailored for diffusion foundation models. Utilizing diversified reward modeling, UniGRPO unifies post-training across both reasoning and generation tasks, ensuring consistent performance improvements. Experimental results demonstrate that MMaDA-8B exhibits strong generalization capabilities as a unified multimodal foundation model. It surpasses powerful models like LLaMA-3-7B and Qwen2-7B in textual reasoning, outperforms Show-o and SEED-X in multimodal understanding, and excels over SDXL and Janus in text-to-image generation. These achievements highlight MMaDA's effectiveness in bridging the gap between pretraining and post-training within unified diffusion architectures, providing a comprehensive framework for future research and development. We open-source our code and trained models at: https://github.com/Gen-Verse/MMaDA

Multimodal generative models that can understand and generate across multiple modalities are dominated by autoregressive (AR) approaches, which process tokens sequentially from left to right, or top to bottom. These models jointly handle images, text, video, and audio for various tasks such as image captioning, question answering, and image generation. In this work, we explore discrete diffusion models as a unified generative formulation in the joint text and image domain, building upon their recent success in text generation. Discrete diffusion models offer several advantages over AR models, including improved control over quality versus diversity of generated samples, the ability to perform joint multimodal inpainting (across both text and image domains), and greater controllability in generation through guidance. Leveraging these benefits, we present the first Unified Multimodal Discrete Diffusion (UniDisc) model which is capable of jointly understanding and generating text and images for a variety of downstream tasks. We compare UniDisc to multimodal AR models, performing a scaling analysis and demonstrating that UniDisc outperforms them in terms of both performance and inference-time compute, enhanced controllability, editability, inpainting, and flexible trade-off between inference time and generation quality. Code and additional visualizations are available at https://unidisc.github.io.

Diffusion models show promise for dynamic scene deblurring; however, existing studies often fail to leverage the intrinsic nature of the blurring process within diffusion models, limiting their full potential. To address it, we present a Blur Diffusion Model (BlurDM), which seamlessly integrates the blur formation process into diffusion for image deblurring. Observing that motion blur stems from continuous exposure, BlurDM implicitly models the blur formation process through a dual-diffusion forward scheme, diffusing both noise and blur onto a sharp image. During the reverse generation process, we derive a dual denoising and deblurring formulation, enabling BlurDM to recover the sharp image by simultaneously denoising and deblurring, given pure Gaussian noise conditioned on the blurred image as input. Additionally, to efficiently integrate BlurDM into deblurring networks, we perform BlurDM in the latent space, forming a flexible prior generation network for deblurring. Extensive experiments demonstrate that BlurDM significantly and consistently enhances existing deblurring methods on four benchmark datasets. The source code is available at https://github.com/Jin-Ting-He/BlurDM.

Gradient descent has proven to be a powerful and effective technique for optimization in numerous machine learning applications. Recent advances in computational neuroscience have shown that learning in standard gradient descent optimization formulation is not consistent with learning in biological systems. This has opened up interesting avenues for building biologically inspired learning techniques. One such approach is inspired by Dale's law, which states that inhibitory and excitatory synapses do not swap roles during the course of learning. The resulting exponential gradient descent optimization scheme leads to log-normally distributed synaptic weights. Interestingly, the density that satisfies the Fokker-Planck equation corresponding to the stochastic differential equation (SDE) with geometric Brownian motion (GBM) is the log-normal density. Leveraging this connection, we start with the SDE governing geometric Brownian motion, and show that discretizing the corresponding reverse-time SDE yields a multiplicative update rule, which surprisingly, coincides with the sampling equivalent of the exponential gradient descent update founded on Dale's law. Furthermore, we propose a new formalism for multiplicative denoising score-matching, subsuming the loss function proposed by Hyvaerinen for non-negative data. Indeed, log-normally distributed data is positive and the proposed score-matching formalism turns out to be a natural fit. This allows for training of score-based models for image data and results in a novel multiplicative update scheme for sample generation starting from a log-normal density. Experimental results on MNIST, Fashion MNIST, and Kuzushiji datasets demonstrate generative capability of the new scheme. To the best of our knowledge, this is the first instance of a biologically inspired generative model employing multiplicative updates, founded on geometric Brownian motion.

Diffusion models achieve state-of-the-art generative performance but are fundamentally bottlenecked by their slow, iterative sampling process. While diffusion distillation techniques enable high-fidelity, few-step generation, traditional objectives often restrict the student's performance by anchoring it solely to the teacher. Recent approaches have attempted to break this ceiling by integrating Reinforcement Learning (RL), typically through a simple summation of distillation and RL objectives. In this work, we propose a novel paradigm by re-conceptualizing distribution matching as a reward, denoted as R_dm. This unified perspective bridges the algorithmic gap between Diffusion Matching Distillation (DMD) and RL, providing several primary benefits. (1) Enhanced Optimization Stability: We introduce Group Normalized Distribution Matching (GNDM), which adapts standard RL group normalization to stabilize R_dm estimation. By leveraging group-mean statistics, GNDM establishes a more robust and effective optimization direction. (2) Seamless Reward Integration: Our reward-centric formulation inherently supports adaptive weighting mechanisms, allowing for the fluid combination of DMD with external reward models. (3) Improved Sampling Efficiency: By aligning with RL principles, the framework readily incorporates Importance Sampling (IS), leading to a significant boost in sampling efficiency. Extensive experiments demonstrate that GNDM outperforms vanilla DMD, reducing the FID by 1.87. Furthermore, our multi-reward variant, GNDMR, surpasses existing baselines by striking an optimal balance between aesthetic quality and fidelity, achieving a peak HPS of 30.37 and a low FID-SD of 12.21. Ultimately, R_dm provides a flexible, stable, and efficient framework for real-time, high-fidelity synthesis. Codes are coming soon.

Diffusion Language Models (DLMs) have recently achieved strong results in text generation. However, their multi-step sampling leads to slow inference, limiting practical use. To address this, we extend Inverse Distillation, a technique originally developed to accelerate continuous diffusion models, to the discrete setting. Nonetheless, this extension introduces both theoretical and practical challenges. From a theoretical perspective, the inverse distillation objective lacks uniqueness guarantees, which may lead to suboptimal solutions. From a practical standpoint, backpropagation in the discrete space is non-trivial and often unstable. To overcome these challenges, we first provide a theoretical result demonstrating that our inverse formulation admits a unique solution, thereby ensuring valid optimization. We then introduce gradient-stable relaxations to support effective training. As a result, experiments on multiple DLMs show that our method, Inverse-distilled Diffusion Language Models (IDLM), reduces the number of inference steps by 4x-64x, while preserving the teacher model's entropy and generative perplexity.

Diffusion language models enable parallel token generation through block-wise decoding, but their irreversible commitments can lead to stagnation, where the reverse diffusion process fails to make further progress under a suboptimal context.We propose Reversible Diffusion Decoding (RDD), a decoding framework that introduces reversibility into block-wise diffusion generation. RDD detects stagnation as a state-dependent failure of the reverse process and enables efficient backtracking to earlier blocks without recomputation via cached model states. To avoid repeated failure trajectories, RDD applies confidence-guided re-masking to selectively reinitialize uncertain tokens while preserving reliable context.This reversible formulation allows decoding to recover from early commitment errors while maintaining the parallel efficiency of diffusion-based generation. Experiments show that RDD improves generation robustness and quality over baselines with minimal computational overhead.

Diffusion models have been extensively leveraged for learning robot skills from demonstrations. These policies are conditioned on several observational modalities such as proprioception, vision and tactile. However, observational modalities have varying levels of influence for different tasks that diffusion polices fail to capture. In this work, we propose 'Factorized Diffusion Policies' abbreviated as FDP, a novel policy formulation that enables observational modalities to have differing influence on the action diffusion process by design. This results in learning policies where certain observations modalities can be prioritized over the others such as vision>tactile or proprioception>vision. FDP achieves modality prioritization by factorizing the observational conditioning for diffusion process, resulting in more performant and robust policies. Our factored approach shows strong performance improvements in low-data regimes with 15% absolute improvement in success rate on several simulated benchmarks when compared to a standard diffusion policy that jointly conditions on all input modalities. Moreover, our benchmark and real-world experiments show that factored policies are naturally more robust with 40% higher absolute success rate across several visuomotor tasks under distribution shifts such as visual distractors or camera occlusions, where existing diffusion policies fail catastrophically. FDP thus offers a safer and more robust alternative to standard diffusion policies for real-world deployment. Videos are available at https://fdp-policy.github.io/fdp-policy/ .

Guided sampling is a vital approach for applying diffusion models in real-world tasks that embeds human-defined guidance during the sampling procedure. This paper considers a general setting where the guidance is defined by an (unnormalized) energy function. The main challenge for this setting is that the intermediate guidance during the diffusion sampling procedure, which is jointly defined by the sampling distribution and the energy function, is unknown and is hard to estimate. To address this challenge, we propose an exact formulation of the intermediate guidance as well as a novel training objective named contrastive energy prediction (CEP) to learn the exact guidance. Our method is guaranteed to converge to the exact guidance under unlimited model capacity and data samples, while previous methods can not. We demonstrate the effectiveness of our method by applying it to offline reinforcement learning (RL). Extensive experiments on D4RL benchmarks demonstrate that our method outperforms existing state-of-the-art algorithms. We also provide some examples of applying CEP for image synthesis to demonstrate the scalability of CEP on high-dimensional data.

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

World models aim to predict plausible futures consistent with past observations, a capability central to planning and decision-making in reinforcement learning. Yet, existing architectures face a fundamental memory trade-off: transformers preserve local detail but are bottlenecked by quadratic attention, while recurrent and state-space models scale more efficiently but compress history at the cost of fidelity. To overcome this trade-off, we suggest decoupling future-past consistency from any single architecture and instead leveraging a set of specialized experts. We introduce a diffusion-based framework that integrates heterogeneous memory models through a contrastive product-of-experts formulation. Our approach instantiates three complementary roles: a short-term memory expert that captures fine local dynamics, a long-term memory expert that stores episodic history in external diffusion weights via lightweight test-time finetuning, and a spatial long-term memory expert that enforces geometric and spatial coherence. This compositional design avoids mode collapse and scales to long contexts without incurring a quadratic cost. Across simulated and real-world benchmarks, our method improves temporal consistency, recall of past observations, and navigation performance, establishing a novel paradigm for building and operating memory-augmented diffusion world models.

Diffusion policy sampling enables reinforcement learning (RL) to represent multimodal action distributions beyond suboptimal unimodal Gaussian policies. However, existing diffusion-based RL methods primarily focus on offline settings for reward maximization, with limited consideration of safety in online settings. To address this gap, we propose Augmented Lagrangian-Guided Diffusion (ALGD), a novel algorithm for off-policy safe RL. By revisiting optimization theory and energy-based model, we show that the instability of primal-dual methods arises from the non-convex Lagrangian landscape. In diffusion-based safe RL, the Lagrangian can be interpreted as an energy function guiding the denoising dynamics. Counterintuitively, direct usage destabilizes both policy generation and training. ALGD resolves this issue by introducing an augmented Lagrangian that locally convexifies the energy landscape, yielding a stabilized policy generation and training process without altering the distribution of the optimal policy. Theoretical analysis and extensive experiments demonstrate that ALGD is both theoretically grounded and empirically effective, achieving strong and stable performance across diverse environments.

Multi-view diffusion models have shown promise in 3D novel view synthesis, but most existing methods adopt a non-autoregressive formulation. This limits their applicability in world modeling, as they only support a fixed number of views and suffer from slow inference due to denoising all frames simultaneously. To address these limitations, we propose CausNVS, a multi-view diffusion model in an autoregressive setting, which supports arbitrary input-output view configurations and generates views sequentially. We train CausNVS with causal masking and per-frame noise, using pairwise-relative camera pose encodings (CaPE) for precise camera control. At inference time, we combine a spatially-aware sliding-window with key-value caching and noise conditioning augmentation to mitigate drift. Our experiments demonstrate that CausNVS supports a broad range of camera trajectories, enables flexible autoregressive novel view synthesis, and achieves consistently strong visual quality across diverse settings. Project page: https://kxhit.github.io/CausNVS.html.

We propose a method to distill a complex multistep diffusion model into a single-step conditional GAN student model, dramatically accelerating inference, while preserving image quality. Our approach interprets diffusion distillation as a paired image-to-image translation task, using noise-to-image pairs of the diffusion model's ODE trajectory. For efficient regression loss computation, we propose E-LatentLPIPS, a perceptual loss operating directly in diffusion model's latent space, utilizing an ensemble of augmentations. Furthermore, we adapt a diffusion model to construct a multi-scale discriminator with a text alignment loss to build an effective conditional GAN-based formulation. E-LatentLPIPS converges more efficiently than many existing distillation methods, even accounting for dataset construction costs. We demonstrate that our one-step generator outperforms cutting-edge one-step diffusion distillation models -- DMD, SDXL-Turbo, and SDXL-Lightning -- on the zero-shot COCO benchmark.

We propose a diffusion distillation method that achieves new state-of-the-art in one-step/few-step 1024px text-to-image generation based on SDXL. Our method combines progressive and adversarial distillation to achieve a balance between quality and mode coverage. In this paper, we discuss the theoretical analysis, discriminator design, model formulation, and training techniques. We open-source our distilled SDXL-Lightning models both as LoRA and full UNet weights.

Score distillation sampling has been pivotal for integrating diffusion models into generation of complex visuals. Despite impressive results it suffers from mode collapse and lack of diversity. To cope with this challenge, we leverage the gradient flow interpretation of score distillation to propose Repulsive Score Distillation (RSD). In particular, we propose a variational framework based on repulsion of an ensemble of particles that promotes diversity. Using a variational approximation that incorporates a coupling among particles, the repulsion appears as a simple regularization that allows interaction of particles based on their relative pairwise similarity, measured e.g., via radial basis kernels. We design RSD for both unconstrained and constrained sampling scenarios. For constrained sampling we focus on inverse problems in the latent space that leads to an augmented variational formulation, that strikes a good balance between compute, quality and diversity. Our extensive experiments for text-to-image generation, and inverse problems demonstrate that RSD achieves a superior trade-off between diversity and quality compared with state-of-the-art alternatives.

Diffusion models have achieved remarkable success in generative tasks but suffer from high computational costs due to their iterative sampling process and quadratic attention costs. Existing training-free acceleration strategies that reduce per-step computation cost, while effectively reducing sampling time, demonstrate low faithfulness compared to the original baseline. We hypothesize that this fidelity gap arises because (a) different prompts correspond to varying denoising trajectory, and (b) such methods do not consider the underlying ODE formulation and its numerical solution. In this paper, we propose Stability-guided Adaptive Diffusion Acceleration (SADA), a novel paradigm that unifies step-wise and token-wise sparsity decisions via a single stability criterion to accelerate sampling of ODE-based generative models (Diffusion and Flow-matching). For (a), SADA adaptively allocates sparsity based on the sampling trajectory. For (b), SADA introduces principled approximation schemes that leverage the precise gradient information from the numerical ODE solver. Comprehensive evaluations on SD-2, SDXL, and Flux using both EDM and DPM++ solvers reveal consistent ge 1.8times speedups with minimal fidelity degradation (LPIPS leq 0.10 and FID leq 4.5) compared to unmodified baselines, significantly outperforming prior methods. Moreover, SADA adapts seamlessly to other pipelines and modalities: It accelerates ControlNet without any modifications and speeds up MusicLDM by 1.8times with sim 0.01 spectrogram LPIPS.

The human-like form of humanoid robots positions them uniquely to achieve the agility and versatility in motor skills that humans possess. Learning from human demonstrations offers a scalable approach to acquiring these capabilities. However, prior works either produce unnatural motions or rely on motion-specific tuning to achieve satisfactory naturalness. Furthermore, these methods are often motion- or goal-specific, lacking the versatility to compose diverse skills, especially when solving unseen tasks. We present BeyondMimic, a framework that scales to diverse motions and carries the versatility to compose them seamlessly in tackling unseen downstream tasks. At heart, a compact motion-tracking formulation enables mastering a wide range of radically agile behaviors, including aerial cartwheels, spin-kicks, flip-kicks, and sprinting, with a single setup and shared hyperparameters, all while achieving state-of-the-art human-like performance. Moving beyond the mere imitation of existing motions, we propose a unified latent diffusion model that empowers versatile goal specification, seamless task switching, and dynamic composition of these agile behaviors. Leveraging classifier guidance, a diffusion-specific technique for test-time optimization toward novel objectives, our model extends its capability to solve downstream tasks never encountered during training, including motion inpainting, joystick teleoperation, and obstacle avoidance, and transfers these skills zero-shot to real hardware. This work opens new frontiers for humanoid robots by pushing the limits of scalable human-like motor skill acquisition from human motion and advancing seamless motion synthesis that achieves generalization and versatility beyond training setups.

Video Diffusion Models (VDMs) can generate high-quality videos, but often struggle with producing temporally coherent motion. Optical flow supervision is a promising approach to address this, with prior works commonly employing warping-based strategies that avoid explicit flow matching. In this work, we explore an alternative formulation, FlowLoss, which directly compares flow fields extracted from generated and ground-truth videos. To account for the unreliability of flow estimation under high-noise conditions in diffusion, we propose a noise-aware weighting scheme that modulates the flow loss across denoising steps. Experiments on robotic video datasets suggest that FlowLoss improves motion stability and accelerates convergence in early training stages. Our findings offer practical insights for incorporating motion-based supervision into noise-conditioned generative models.

This paper puts forward an integrated microstructure design methodology that replaces the common existing design approaches: 1) reconstruction of microstructures, 2) analyzing and quantifying material properties, and 3) inverse design of materials using deep-learned generative and surrogate models. The long-standing issue of microstructure reconstruction is well addressed in this study using a new class of state-of-the-art generative model, the diffusion-based generative model (DGM). Moreover, the conditional formulation of DGM for guidance to the embedded desired material properties with a transformer-based attention mechanism enables the inverse design of multifunctional composites. A convolutional neural network (CNN)-based surrogate model is utilized to analyze the nonlinear material behavior to facilitate the prediction of material properties for building microstructure-property linkages. Combined, these generative and surrogate models enable large data processing and database construction that is often not affordable with resource-intensive finite element method (FEM)-based direct numerical simulation (DNS) and iterative reconstruction methods. An example case is presented to demonstrate the effectiveness of the proposed approach, which is designing mechanoluminescence (ML) particulate composites made of europium and dysprosium ions. The results show that the inversely-designed multiple ML microstructure candidates with the proposed generative and surrogate models meet the multiple design requirements (e.g., volume fraction, elastic constant, and light sensitivity). The evaluation of the generated samples' quality and the surrogate models' performance using appropriate metrics are also included. This assessment demonstrates that the proposed integrated methodology offers an end-to-end solution for practical material design applications.

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.

Diffusion models are often introduced from multiple perspectives, such as VAEs, score matching, or flow matching, accompanied by dense and technically demanding mathematics that can be difficult for beginners to grasp. One classic question is: how does the reverse process invert the forward process to generate data from pure noise? This article systematically organizes the diffusion model from a fresh Langevin perspective, offering a simpler, clearer, and more intuitive answer. We also address the following questions: how can ODE-based and SDE-based diffusion models be unified under a single framework? Why are diffusion models theoretically superior to ordinary VAEs? Why is flow matching not fundamentally simpler than denoising or score matching, but equivalent under maximum-likelihood? We demonstrate that the Langevin perspective offers clear and straightforward answers to these questions, bridging existing interpretations of diffusion models, showing how different formulations can be converted into one another within a common framework, and offering pedagogical value for both learners and experienced researchers seeking deeper intuition.

In the task of reference-based image inpainting, an additional reference image is provided to restore a damaged target image to its original state. The advancement of diffusion models, particularly Stable Diffusion, allows for simple formulations in this task. However, existing diffusion-based methods often lack explicit constraints on the correlation between the reference and damaged images, resulting in lower faithfulness to the reference images in the inpainting results. In this work, we propose CorrFill, a training-free module designed to enhance the awareness of geometric correlations between the reference and target images. This enhancement is achieved by guiding the inpainting process with correspondence constraints estimated during inpainting, utilizing attention masking in self-attention layers and an objective function to update the input tensor according to the constraints. Experimental results demonstrate that CorrFill significantly enhances the performance of multiple baseline diffusion-based methods, including state-of-the-art approaches, by emphasizing faithfulness to the reference images.

Diffusion models have recently been extended to language generation through Masked Diffusion Language Models (MDLMs), which achieve performance competitive with strong autoregressive models. However, MDLMs tend to degrade in the few-step regime and cannot directly adopt existing few-step distillation methods designed for continuous diffusion models, as they lack the intrinsic property of mapping from noise to data. Recent Uniform-state Diffusion Models (USDMs), initialized from a uniform prior, alleviate some limitations but still suffer from complex loss formulations that hinder scalability. In this work, we propose a simplified denoising-based loss for USDMs that optimizes only noise-replaced tokens, stabilizing training and matching ELBO-level performance. Furthermore, by framing denoising as self-supervised learning, we introduce a simple modification to our denoising loss with contrastive-inspired negative gradients, which is practical and yield additional improvements in generation quality.

Diffusion Transformers (DiT) have become a leading architecture in image generation. However, the quadratic complexity of attention mechanisms, which are responsible for modeling token-wise relationships, results in significant latency when generating high-resolution images. To address this issue, we aim at a linear attention mechanism in this paper that reduces the complexity of pre-trained DiTs to linear. We begin our exploration with a comprehensive summary of existing efficient attention mechanisms and identify four key factors crucial for successful linearization of pre-trained DiTs: locality, formulation consistency, high-rank attention maps, and feature integrity. Based on these insights, we introduce a convolution-like local attention strategy termed CLEAR, which limits feature interactions to a local window around each query token, and thus achieves linear complexity. Our experiments indicate that, by fine-tuning the attention layer on merely 10K self-generated samples for 10K iterations, we can effectively transfer knowledge from a pre-trained DiT to a student model with linear complexity, yielding results comparable to the teacher model. Simultaneously, it reduces attention computations by 99.5% and accelerates generation by 6.3 times for generating 8K-resolution images. Furthermore, we investigate favorable properties in the distilled attention layers, such as zero-shot generalization cross various models and plugins, and improved support for multi-GPU parallel inference. Models and codes are available here: https://github.com/Huage001/CLEAR.

In order to improve the quality of synthesized videos, currently, one predominant method involves retraining an expert diffusion model and then implementing a noising-denoising process for refinement. Despite the significant training costs, maintaining consistency of content between the original and enhanced videos remains a major challenge. To tackle this challenge, we propose a novel formulation that considers both visual quality and consistency of content. Consistency of content is ensured by a proposed loss function that maintains the structure of the input, while visual quality is improved by utilizing the denoising process of pretrained diffusion models. To address the formulated optimization problem, we have developed a plug-and-play noise optimization strategy, referred to as Noise Calibration. By refining the initial random noise through a few iterations, the content of original video can be largely preserved, and the enhancement effect demonstrates a notable improvement. Extensive experiments have demonstrated the effectiveness of the proposed method.

We present Assembler, a scalable and generalizable framework for 3D part assembly that reconstructs complete objects from input part meshes and a reference image. Unlike prior approaches that mostly rely on deterministic part pose prediction and category-specific training, Assembler is designed to handle diverse, in-the-wild objects with varying part counts, geometries, and structures. It addresses the core challenges of scaling to general 3D part assembly through innovations in task formulation, representation, and data. First, Assembler casts part assembly as a generative problem and employs diffusion models to sample plausible configurations, effectively capturing ambiguities arising from symmetry, repeated parts, and multiple valid assemblies. Second, we introduce a novel shape-centric representation based on sparse anchor point clouds, enabling scalable generation in Euclidean space rather than SE(3) pose prediction. Third, we construct a large-scale dataset of over 320K diverse part-object assemblies using a synthesis and filtering pipeline built on existing 3D shape repositories. Assembler achieves state-of-the-art performance on PartNet and is the first to demonstrate high-quality assembly for complex, real-world objects. Based on Assembler, we further introduce an interesting part-aware 3D modeling system that generates high-resolution, editable objects from images, demonstrating potential for interactive and compositional design. Project page: https://assembler3d.github.io

We present Flex4DHuman, a multi-view video diffusion model that transforms a monocular or sparse multi-view video of a dynamic subject into synchronized dense multi-view videos using only relative camera-pose conditioning. Unlike prior human-centric methods that rely on skeletons, depth maps, normals, or rendered target-view geometry, Flex4DHuman requires no explicit geometry priors and instead conditions generation through relative camera-pose positional encoding. The generated videos can be directly ingested by downstream reconstruction pipelines to create dynamic 4D Gaussian splats. Built on the Wan 2.1 1.3B text-to-video model, Flex4DHuman preserves the backbone architecture and encodes camera and view information through a five-axis positional encoding that extends spatio-temporal RoPE with view indices and continuous SE(3) relative camera geometry. A three-stage curriculum progressively trains the model for pose following, flexible reference-to-target view generation, and temporal rollout. To support temporal rollout, we train with clean historical target-view tokens. We also add multi-view captions to enable test-time text control. Combined with an off-the-shelf 4D Gaussian Splatting stage, our framework lifts monocular static-camera videos into dynamic 4D Gaussian splats. Experiments on DNA-Rendering and ActorsHQ show that Flex4DHuman surpasses prior state-of-the-art methods, while the same formulation generalizes to animal categories after mixed human-animal training. These capabilities make Flex4DHuman a practical step toward scalable 4D content creation from casual monocular videos for simulation, gaming, AR/VR, and video re-shooting.

Diffusion transformers (DiTs) have emerged as a powerful architecture for high-fidelity image generation, yet the quadratic cost of self-attention poses a major scalability bottleneck. To address this, linear attention mechanisms have been adopted to reduce computational cost; unfortunately, the resulting linear diffusion transformers (LiTs) models often come at the expense of generative performance, frequently producing over-smoothed attention weights that limit expressiveness. In this work, we introduce Dynamic Differential Linear Attention (DyDiLA), a novel linear attention formulation that enhances the effectiveness of LiTs by mitigating the oversmoothing issue and improving generation quality. Specifically, the novelty of DyDiLA lies in three key designs: (i) dynamic projection module, which facilitates the decoupling of token representations by learning with dynamically assigned knowledge; (ii) dynamic measure kernel, which provides a better similarity measurement to capture fine-grained semantic distinctions between tokens by dynamically assigning kernel functions for token processing; and (iii) token differential operator, which enables more robust query-to-key retrieval by calculating the differences between the tokens and their corresponding information redundancy produced by dynamic measure kernel. To capitalize on DyDiLA, we introduce a refined LiT, termed DyDi-LiT, that systematically incorporates our advancements. Extensive experiments show that DyDi-LiT consistently outperforms current state-of-the-art (SOTA) models across multiple metrics, underscoring its strong practical potential.

Despite the remarkable success, recent reconstruction-based anomaly detection (AD) methods via diffusion modeling still involve fine-grained noise-strength tuning and computationally expensive multi-step denoising, leading to a fundamental tension between fidelity and efficiency. In this paper, we propose InvAD, a novel inversion-based anomaly detection approach ("detection via noising in latent space") that circumvents explicit reconstruction. Importantly, we contend that the limitations in prior reconstruction-based methods originate from the prevailing "detection via denoising in RGB space" paradigm. To address this, we model AD under a reconstruction-free formulation, which directly infers the final latent variable corresponding to the input image via DDIM inversion, and then measures the deviation based on the known prior distribution for anomaly scoring. Specifically, in approximating the original probability flow ODE using the Euler method, we enforce only a few inversion steps to noise the clean image to pursue inference efficiency. As the added noise is adaptively derived with the learned diffusion model, the original features for the clean testing image can still be leveraged to yield high detection accuracy. We perform extensive experiments and detailed analyses across four widely used industrial and medical AD benchmarks under the unsupervised unified setting to demonstrate the effectiveness of our model, achieving state-of-the-art AD performance and approximately 2x inference-time speedup without diffusion distillation.

Recent years have witnessed the rapid progress and broad application of diffusion probabilistic models (DPMs). Sampling from DPMs can be viewed as solving an ordinary differential equation (ODE). Despite the promising performance, the generation of DPMs usually consumes much time due to the large number of function evaluations (NFE). Though recent works have accelerated the sampling to around 20 steps with high-order solvers, the sample quality with less than 10 NFE can still be improved. In this paper, we propose a unified sampling framework (USF) to study the optional strategies for solver. Under this framework, we further reveal that taking different solving strategies at different timesteps may help further decrease the truncation error, and a carefully designed solver schedule has the potential to improve the sample quality by a large margin. Therefore, we propose a new sampling framework based on the exponential integral formulation that allows free choices of solver strategy at each step and design specific decisions for the framework. Moreover, we propose S^3, a predictor-based search method that automatically optimizes the solver schedule to get a better time-quality trade-off of sampling. We demonstrate that S^3 can find outstanding solver schedules which outperform the state-of-the-art sampling methods on CIFAR-10, CelebA, ImageNet, and LSUN-Bedroom datasets. Specifically, we achieve 2.69 FID with 10 NFE and 6.86 FID with 5 NFE on CIFAR-10 dataset, outperforming the SOTA method significantly. We further apply S^3 to Stable-Diffusion model and get an acceleration ratio of 2times, showing the feasibility of sampling in very few steps without retraining the neural network.

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.

It is well known that many open-released foundational diffusion models have difficulty in generating images that substantially depart from average brightness, despite such images being present in the training data. This is due to an inconsistency: while denoising starts from pure Gaussian noise during inference, the training noise schedule retains residual data even in the final timestep distribution, due to difficulties in numerical conditioning in mainstream formulation, leading to unintended bias during inference. To mitigate this issue, certain epsilon-prediction models are combined with an ad-hoc offset-noise methodology. In parallel, some contemporary models have adopted zero-terminal SNR noise schedules together with v-prediction, which necessitate major alterations to pre-trained models. However, such changes risk destabilizing a large multitude of community-driven applications anchored on these pre-trained models. In light of this, our investigation revisits the fundamental causes, leading to our proposal of an innovative and principled remedy, called One More Step (OMS). By integrating a compact network and incorporating an additional simple yet effective step during inference, OMS elevates image fidelity and harmonizes the dichotomy between training and inference, while preserving original model parameters. Once trained, various pre-trained diffusion models with the same latent domain can share the same OMS module.

Reinforcement Learning (RL) has emerged as a central paradigm for advancing Large Language Models (LLMs), where pre-training and RL post-training share the same log-likelihood formulation. In contrast, recent RL approaches for diffusion models, most notably Denoising Diffusion Policy Optimization (DDPO), optimize an objective different from the pretraining objectives--score/flow matching loss. In this work, we establish a novel theoretical analysis: DDPO is an implicit form of score/flow matching with noisy targets, which increases variance and slows convergence. Building on this analysis, we introduce Advantage Weighted Matching (AWM), a policy-gradient method for diffusion. It uses the same score/flow-matching loss as pretraining to obtain a lower-variance objective and reweights each sample by its advantage. In effect, AWM raises the influence of high-reward samples and suppresses low-reward ones while keeping the modeling objective identical to pretraining. This unifies pretraining and RL conceptually and practically, is consistent with policy-gradient theory, reduces variance, and yields faster convergence. This simple yet effective design yields substantial benefits: on GenEval, OCR, and PickScore benchmarks, AWM delivers up to a 24times speedup over Flow-GRPO (which builds on DDPO), when applied to Stable Diffusion 3.5 Medium and FLUX, without compromising generation quality. Code is available at https://github.com/scxue/advantage_weighted_matching.

We introduce MVGenMaster, a multi-view diffusion model enhanced with 3D priors to address versatile Novel View Synthesis (NVS) tasks. MVGenMaster leverages 3D priors that are warped using metric depth and camera poses, significantly enhancing both generalization and 3D consistency in NVS. Our model features a simple yet effective pipeline that can generate up to 100 novel views conditioned on variable reference views and camera poses with a single forward process. Additionally, we have developed a comprehensive large-scale multi-view image dataset called MvD-1M, comprising up to 1.6 million scenes, equipped with well-aligned metric depth to train MVGenMaster. Moreover, we present several training and model modifications to strengthen the model with scaled-up datasets. Extensive evaluations across in- and out-of-domain benchmarks demonstrate the effectiveness of our proposed method and data formulation. Models and codes will be released at https://github.com/ewrfcas/MVGenMaster/.

Diffusion and flow-based models have become the de facto approaches for generating continuous data, e.g., in domains such as images and videos. Their success has attracted growing interest in applying them to language modeling. Unlike their image-domain counterparts, today's leading diffusion language models (DLMs) primarily operate over discrete tokens. In this paper, we show that continuous DLMs can be made effective with minimal adaptation to the discrete domain. We propose Embedded Language Flows (ELF), a class of diffusion models in continuous embedding space based on continuous-time Flow Matching. Unlike existing DLMs, ELF predominantly stays within the continuous embedding space until the final time step, where it maps to discrete tokens using a shared-weight network. This formulation makes it straightforward to adapt established techniques from image-domain diffusion models, e.g., classifier-free guidance (CFG). Experiments show that ELF substantially outperforms leading discrete and continuous DLMs, achieving better generation quality with fewer sampling steps. These results suggest that ELF offers a promising path toward effective continuous DLMs.

Text-to-image diffusion models are nothing but a revolution, allowing anyone, even without design skills, to create realistic images from simple text inputs. With powerful personalization tools like DreamBooth, they can generate images of a specific person just by learning from his/her few reference images. However, when misused, such a powerful and convenient tool can produce fake news or disturbing content targeting any individual victim, posing a severe negative social impact. In this paper, we explore a defense system called Anti-DreamBooth against such malicious use of DreamBooth. The system aims to add subtle noise perturbation to each user's image before publishing in order to disrupt the generation quality of any DreamBooth model trained on these perturbed images. We investigate a wide range of algorithms for perturbation optimization and extensively evaluate them on two facial datasets over various text-to-image model versions. Despite the complicated formulation of DreamBooth and Diffusion-based text-to-image models, our methods effectively defend users from the malicious use of those models. Their effectiveness withstands even adverse conditions, such as model or prompt/term mismatching between training and testing. Our code will be available at https://github.com/VinAIResearch/Anti-DreamBooth.git{https://github.com/VinAIResearch/Anti-DreamBooth.git}.

Autoregressive video diffusion models provide a natural formulation for streaming and variable-length video generation by conditioning newly generated frames on previously generated content. However, extending these models to minute-level generation remains challenging: the limited KV-cache budget prevents the model from retaining the full history, while repeatedly conditioning on self-generated frames induces a context distribution shift that accumulates over time, leading to visual artifacts, quality degradation, and temporal drift. In this paper, we propose TetherCache, a training-free and plug-and-play cache management strategy for drift-resistant long video generation. TetherCache organizes the cache into sink, memory, and recent regions, and introduces two complementary mechanisms. First, GRAB (Gated Recall with Attention-Diversity Balancing) selects long-range memory frames using a gated score that combines attention-based relevance with temporal diversity, preserving informative yet diverse historical context under a fixed cache budget. Second, TAME (Trusted Alignment via Memory Editing) lightly edits newly recalled memory tokens by aligning their statistics to a trusted context distribution, reducing the pollution caused by drifted historical features. Built on Self-Forcing, TetherCache consistently improves long-video generation quality on VBench-Long across 30s, 60s, and 240s settings. In particular, for 240s generation, it substantially improves overall and semantic scores while reducing quality drift from 7.84 to 1.33, demonstrating its effectiveness for stable long-horizon autoregressive video diffusion.

Diffusion models and their variations, such as rectified flows, generate diverse and high-quality images, but they are still hindered by slow iterative sampling caused by the highly curved generative paths they learn. An important cause of high curvature, as shown by previous work, is independence between the source distribution (standard Gaussian) and the data distribution. In this work, we tackle this limitation by two complementary contributions. First, we attempt to break away from the standard Gaussian assumption by introducing κ-FC, a general formulation that conditions the source distribution on an arbitrary signal κ that aligns it better with the data distribution. Then, we present MixFlow, a simple but effective training strategy that reduces the generative path curvatures and considerably improves sampling efficiency. MixFlow trains a flow model on linear mixtures of a fixed unconditional distribution and a κ-FC-based distribution. This simple mixture improves the alignment between the source and data, provides better generation quality with less required sampling steps, and accelerates the training convergence considerably. On average, our training procedure improves the generation quality by 12\% in FID compared to standard rectified flow and 7\% compared to previous baselines under a fixed sampling budget. Code available at: https://github.com/NazirNayal8/MixFlow{https://github.com/NazirNayal8/MixFlow}

Diffusion models are rapidly redefining 3D anomaly detection in point cloud data. As 3D sensing becomes integral to modern manufacturing, reliable anomaly detection is essential for high-throughput quality assurance and process control. Yet practical deployment on resource-constrained, latency-critical systems remains limited. Existing methods are often computationally prohibitive or unreliable in complex, unmasked regions, and diffusion pipelines are inherently bottlenecked by iterative denoising. In this work, we address this bottleneck by reformulating reconstructionbased anomaly detection through consistency learning, enabling direct prediction of anomaly-free geometry in one or two network evaluations. We further introduce a novel hybrid loss formulation that explicitly enforces reconstruction toward clean data. This design substantially reduces inference cost, achieving up to 80x faster runtime than the current state-of-the-art method, without GPU acceleration, while preserving strong detection performance. It outperforms R3D-AD on Anomaly-ShapeNet with 76.20% I-AUROC and remains competitive on Real3DAD with 72.80% I-AUROC, enabling efficient, low-latency anomaly detection on resource-constrained platforms, including drones, smart industrial cameras, and other edge devices.

Recent diffusion and flow matching models have demonstrated strong capabilities in image generation and editing by progressively removing noise through iterative sampling. While this enables flexible inversion for semantic-preserving edits, few-step sampling regimes suffer from poor forward process approximation, leading to degraded editing quality. Existing few-step inversion methods often rely on pretrained generators and auxiliary modules, limiting scalability and generalization across different architectures. To address these limitations, we propose BiFM (Bidirectional Flow Matching), a unified framework that jointly learns generation and inversion within a single model. BiFM directly estimates average velocity fields in both ``image to noise" and ``noise to image" directions, constrained by a shared instantaneous velocity field derived from either predefined schedules or pretrained multi-step diffusion models. Additionally, BiFM introduces a novel training strategy using continuous time-interval supervision, stabilized by a bidirectional consistency objective and a lightweight time-interval embedding. This bidirectional formulation also enables one-step inversion and can integrate seamlessly into popular diffusion and flow matching backbones. Across diverse image editing and generation tasks, BiFM consistently outperforms existing few-step approaches, achieving superior performance and editability.

Score-based generative models (SGMs) have recently shown impressive results for difficult generative tasks such as the unconditional and conditional generation of natural images and audio signals. In this work, we extend these models to the complex short-time Fourier transform (STFT) domain, proposing a novel training task for speech enhancement using a complex-valued deep neural network. We derive this training task within the formalism of stochastic differential equations (SDEs), thereby enabling the use of predictor-corrector samplers. We provide alternative formulations inspired by previous publications on using generative diffusion models for speech enhancement, avoiding the need for any prior assumptions on the noise distribution and making the training task purely generative which, as we show, results in improved enhancement performance.

Most recent advances in 3D generative modeling rely on diffusion or flow-matching formulations. We instead explore a fully autoregressive alternative and introduce GaussianGPT, a transformer-based model that directly generates 3D Gaussians via next-token prediction, thus facilitating full 3D scene generation. We first compress Gaussian primitives into a discrete latent grid using a sparse 3D convolutional autoencoder with vector quantization. The resulting tokens are serialized and modeled using a causal transformer with 3D rotary positional embedding, enabling sequential generation of spatial structure and appearance. Unlike diffusion-based methods that refine scenes holistically, our formulation constructs scenes step-by-step, naturally supporting completion, outpainting, controllable sampling via temperature, and flexible generation horizons. This formulation leverages the compositional inductive biases and scalability of autoregressive modeling while operating on explicit representations compatible with modern neural rendering pipelines, positioning autoregressive transformers as a complementary paradigm for controllable and context-aware 3D generation.

Text-to-image (T2I) models excel on single-entity prompts but struggle with multi-subject descriptions, often showing attribute leakage, identity entanglement, and subject omissions. We introduce the first theoretical framework with a principled, optimizable objective for steering sampling dynamics toward multi-subject fidelity. Viewing flow matching (FM) through stochastic optimal control (SOC), we formulate subject disentanglement as control over a trained FM sampler. This yields two architecture-agnostic algorithms: (i) a training-free test-time controller that perturbs the base velocity with a single-pass update, and (ii) Adjoint Matching, a lightweight fine-tuning rule that regresses a control network to a backward adjoint signal while preserving base-model capabilities. The same formulation unifies prior attention heuristics, extends to diffusion models via a flow-diffusion correspondence, and provides the first fine-tuning route explicitly designed for multi-subject fidelity. Empirically, on Stable Diffusion 3.5, FLUX, and Stable Diffusion XL, both algorithms consistently improve multi-subject alignment while maintaining base-model style. Test-time control runs efficiently on commodity GPUs, and fine-tuned controllers trained on limited prompts generalize to unseen ones. We further highlight FOCUS (Flow Optimal Control for Unentangled Subjects), which achieves state-of-the-art multi-subject fidelity across models.

Recovering pixel-wise geometric properties from a single image is fundamentally ill-posed due to appearance ambiguity and non-injective mappings between 2D observations and 3D structures. While discriminative regression models achieve strong performance through large-scale supervision, their success is bounded by the scale, quality and diversity of available data and limited physical reasoning. Recent diffusion models exhibit powerful world priors that encode geometry and semantics learned from massive image-text data, yet directly reusing their stochastic generative formulation is suboptimal for deterministic geometric inference: the former is optimized for diverse and high-fidelity image generation, whereas the latter requires stable and accurate predictions. In this work, we propose Lotus-2, a two-stage deterministic framework for stable, accurate and fine-grained geometric dense prediction, aiming to provide an optimal adaption protocol to fully exploit the pre-trained generative priors. Specifically, in the first stage, the core predictor employs a single-step deterministic formulation with a clean-data objective and a lightweight local continuity module (LCM) to generate globally coherent structures without grid artifacts. In the second stage, the detail sharpener performs a constrained multi-step rectified-flow refinement within the manifold defined by the core predictor, enhancing fine-grained geometry through noise-free deterministic flow matching. Using only 59K training samples, less than 1% of existing large-scale datasets, Lotus-2 establishes new state-of-the-art results in monocular depth estimation and highly competitive surface normal prediction. These results demonstrate that diffusion models can serve as deterministic world priors, enabling high-quality geometric reasoning beyond traditional discriminative and generative paradigms.

We present SyncLight, the first method to enable consistent, parametric relighting across multiple uncalibrated views of a static scene. While single-view relighting has advanced significantly, existing generative approaches struggle to maintain the rigorous lighting consistency essential for multi-camera broadcasts, stereoscopic cinema, and virtual production. SyncLight addresses this by enabling precise control over light intensity and color across a multi-view capture of a scene, conditioned on a single reference edit. Our method leverages a multi-view diffusion transformer trained using a latent bridge matching formulation, achieving high-fidelity relighting of the entire image set in a single inference step. To facilitate training, we introduce a large-scale hybrid dataset comprising diverse synthetic environments -- curated from existing sources and newly designed scenes -- alongside high-fidelity, real-world multi-view captures under calibrated illumination. Surprisingly, though trained only on image pairs, SyncLight generalizes zero-shot to an arbitrary number of viewpoints, effectively propagating lighting changes across all views, without requiring camera pose information. SyncLight enables practical relighting workflows for multi-view capture systems.

Sparse-Linear Attention (SLA) combines sparse and linear attention to accelerate diffusion models and has shown strong performance in video generation. However, (i) SLA relies on a heuristic split that assigns computations to the sparse or linear branch based on attention-weight magnitude, which can be suboptimal. Additionally, (ii) after formally analyzing the attention error in SLA, we identify a mismatch between SLA and a direct decomposition into sparse and linear attention. We propose SLA2, which introduces (I) a learnable router that dynamically selects whether each attention computation should use sparse or linear attention, (II) a more faithful and direct sparse-linear attention formulation that uses a learnable ratio to combine the sparse and linear attention branches, and (III) a sparse + low-bit attention design, where low-bit attention is introduced via quantization-aware fine-tuning to reduce quantization error. Experiments show that on video diffusion models, SLA2 can achieve 97% attention sparsity and deliver an 18.6x attention speedup while preserving generation quality.

Recently, a series of papers proposed deep learning-based approaches to sample from unnormalized target densities using controlled diffusion processes. In this work, we identify these approaches as special cases of the Schr\"odinger bridge problem, seeking the most likely stochastic evolution between a given prior distribution and the specified target. We further generalize this framework by introducing a variational formulation based on divergences between path space measures of time-reversed diffusion processes. This abstract perspective leads to practical losses that can be optimized by gradient-based algorithms and includes previous objectives as special cases. At the same time, it allows us to consider divergences other than the reverse Kullback-Leibler divergence that is known to suffer from mode collapse. In particular, we propose the so-called log-variance loss, which exhibits favorable numerical properties and leads to significantly improved performance across all considered approaches.