Diffusion Models

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Diffusion models learn a data distribution by gradually corrupting examples with noise and training a denoiser to reverse that process. Major approaches include DDPMs and score-based SDEs, latent diffusion and diffusion Transformers, flow and consistency methods, and discrete masked or continuous-time Markov diffusion; conditioning and guidance adapt them to specific tasks. They are used for images, video, audio, language, molecules, and scientific forecasting, with evaluations ranging from ImageNet FID to language perplexity and domain-specific measures of accuracy and uncertainty. A central tension is how to make sampling faster and generation more controllable without sacrificing quality, calibration, or diversity, while theory and ongoing audits address generalization, memorization, and privacy.

Latest papers

1,192 papers152 papers in the last four weeks, up 77% on the four weeks before. 0.9% of all new papers.

Feb 23, 2026

SemanticNVS: Improving Semantic Scene Understanding in Generative Novel View Synthesis

We present SemanticNVS, a camera-conditioned multi-view diffusion model for novel view synthesis (NVS), which improves generation quality and consistency by integrating pre-trained semantic feature extractors. Existing NVS methods perform well for views near the input view, however, they tend to generate semantically implausible and distorted images under long-range camera motion, revealing severe degradation. We speculate that this degradation is due to current models failing to fully understand their conditioning or intermediate generated scene content. Here, we propose to integrate pre-trained semantic feature extractors to incorporate stronger scene semantics as conditioning to achieve high-quality generation even at distant viewpoints. We investigate two different strategies, (1) warped semantic features and (2) an alternating scheme of understanding and generation at each denoising step. Experimental results on multiple datasets demonstrate the clear qualitative and quantitative (4.69%-15.26% in FID) improvement over state-of-the-art alternatives.

Xinya Chen, Christopher Wewer, Jiahao Xie +2

Max Planck Institute for Informatics, Saarland Informatics Campus, Germany

Novel View Synthesis Multi-View Image Synthesis Diffusion Models

Feb 23, 2026

Expanding the Role of Diffusion Models for Robust Classifier Training

Incorporating diffusion-generated synthetic data into adversarial training (AT) has been shown to substantially improve the training of robust image classifiers. In this work, we extend the role of diffusion models beyond merely generating synthetic data, examining whether their internal representations, which encode meaningful features of the data, can provide additional benefits for robust classifier training. Through systematic experiments, we show that diffusion models offer representations that are both diverse and partially robust, and that explicitly incorporating diffusion representations as an auxiliary learning signal during AT consistently improves robustness across settings. Furthermore, our representation analysis indicates that incorporating diffusion models into AT encourages more disentangled features, while diffusion representations and diffusion-generated synthetic data play complementary roles in shaping representations. Experiments on CIFAR-10, CIFAR-100, and ImageNet validate these findings, demonstrating the effectiveness of jointly leveraging diffusion representations and synthetic data within AT.

Pin-Han Huang, Shang-Tse Chen, Hsuan-Tien Lin

National Taiwan University

Adversarial Robustness Adversarial Training Diffusion Models Synthetic Data Augmentation

Feb 23, 2026

PerturbDiff: Functional Diffusion for Single-Cell Perturbation Modeling

Building Virtual Cells that can accurately simulate cellular responses to perturbations is a long-standing goal in systems biology. A fundamental challenge is that high-throughput single-cell sequencing is destructive: the same cell cannot be observed both before and after a perturbation. Thus, perturbation prediction requires mapping unpaired control and perturbed populations. Existing models address this by learning maps between distributions, but typically assume a single fixed response distribution when conditioned on observed cellular context (e.g., cell type) and the perturbation type. In reality, responses vary systematically due to unobservable latent factors such as microenvironmental fluctuations and complex batch effects, forming a manifold of possible distributions for the same observed conditions. To account for this variability, we introduce PerturbDiff, which shifts modeling from individual cells to entire distributions. By embedding distributions as points in a Hilbert space, we define a diffusion-based generative process operating directly over probability distributions. This allows PerturbDiff to capture population-level response shifts across hidden factors. Benchmarks on established datasets show that PerturbDiff achieves state-of-the-art performance in single-cell response prediction and generalizes substantially better to unseen perturbations. See our project page (https://katarinayuan.github.io/PerturbDiff-ProjectPage/), where code and data will be made publicly available (https://github.com/DeepGraphLearning/PerturbDiff).

Xinyu Yuan, Xixian Liu, Ya Shi Zhang +3

Mila - Québec AI Institute · University of Montréal · University of Ottawa +3

Single-Cell Perturbation Modeling Single-Cell Transcriptomics Diffusion Models Conditional Diffusion Models

Feb 23, 2026

DICArt: Advancing Category-level Articulated Object Pose Estimation in Discrete State-Spaces

Articulated object pose estimation is a core task in embodied AI. Existing methods typically regress poses in a continuous space, but often struggle with 1) navigating a large, complex search space and 2) failing to incorporate intrinsic kinematic constraints. In this work, we introduce DICArt (DIsCrete Diffusion for Articulation Pose Estimation), a novel framework that formulates pose estimation as a conditional discrete diffusion process. Instead of operating in a continuous domain, DICArt progressively denoises a noisy pose representation through a learned reverse diffusion procedure to recover the GT pose. To improve modeling fidelity, we propose a flexible flow decider that dynamically determines whether each token should be denoised or reset, effectively balancing the real and noise distributions during diffusion. Additionally, we incorporate a hierarchical kinematic coupling strategy, estimating the pose of each rigid part hierarchically to respect the object's kinematic structure. We validate DICArt on both synthetic and real-world datasets. Experimental results demonstrate its superior performance and robustness. By integrating discrete generative modeling with structural priors, DICArt offers a new paradigm for reliable category-level 6D pose estimation in complex environments.

Li Zhang, Mingyu Mei, Ailing Wang +7

University of Science and Technology of China · Zhejiang University · East China Normal University +6

Object Pose Estimation Diffusion Models Articulated Object Reconstruction

Feb 23, 2026

Variational Trajectory Optimization of Anisotropic Diffusion Schedules

We introduce a variational framework for diffusion models with anisotropic noise schedules parameterized by a matrix-valued path

M_t(θ)

that allocates noise across subspaces. Central to our framework is a trajectory-level objective that jointly trains the score network and learns

M_t(θ)

, which encompasses general parameterization classes of matrix-valued noise schedules. We further derive an estimator for the derivative with respect to

θ

of the score that enables efficient optimization of the

M_t(θ)

schedule. For inference, we develop an efficiently-implementable reverse-ODE solver that is an anisotropic generalization of the second-order Heun discretization algorithm. Across CIFAR-10, AFHQv2, FFHQ, and ImageNet-64, our method consistently improves upon the baseline EDM model in all NFE regimes. Code is available at https://github.com/lizeyu090312/anisotropic-diffusion-paper.

Pengxi Liu, Zeyu Michael Li, Xiang Cheng

Department of Electrical and Computer Engineering, Duke University

Diffusion Models Diffusion Timestep Scheduling

Feb 23, 2026

Regressor-guided Diffusion Model for De Novo Peptide Sequencing with Explicit Mass Control

The discovery of novel proteins relies on sensitive protein identification, for which de novo peptide sequencing (DNPS) from mass spectra is a crucial approach. While deep learning has advanced DNPS, existing models inadequately enforce the fundamental mass consistency constraint, that a predicted peptide's mass must match the experimental measured precursor mass. Previous DNPS methods often treat this critical information as a simple input feature or use it in post-processing, leading to numerous implausible predictions that do not adhere to this fundamental physical property. To address this limitation, we introduce DiffuNovo, a novel regressor-guided diffusion model for de novo peptide sequencing that provides explicit peptide-level mass control. Our approach integrates the mass constraint at two critical stages: during training, a novel peptide-level mass loss guides model optimization, while at inference, regressor-based guidance from gradient-based updates in the latent space steers the generation to compel the predicted peptide adheres to the mass constraint. Comprehensive evaluations on established benchmarks demonstrate that DiffuNovo surpasses state-of-the-art methods in DNPS accuracy. Additionally, as the first DNPS model to employ a diffusion model as its core backbone, DiffuNovo leverages the powerful controllability of diffusion architecture and achieves a significant reduction in mass error, thereby producing much more physically plausible peptides. These innovations represent a substantial advancement toward robust and broadly applicable DNPS. The source code is available in the supplementary material.

Shaorong Chen, Jingbo Zhou, Jun Xia

Zhejiang University, Hangzhou, China, 310058 · AI Lab, Westlake University, Hangzhou, China, 310030 · AIMS Lab, The Hong Kong University of Science and Technology (Guangzhou), Guangzhou, China, 511453 +1

Mass Spectrometry Diffusion Model Guidance Diffusion Models

Feb 22, 2026

VLM-Guided Group Preference Alignment for Diffusion-based Human Mesh Recovery

Human mesh recovery (HMR) from a single RGB image is inherently ambiguous, as multiple 3D poses can correspond to the same 2D observation. Recent diffusion-based methods tackle this by generating various hypotheses, but often sacrifice accuracy. They yield predictions that are either physically implausible or drift from the input image, especially under occlusion or in cluttered, in-the-wild scenes. To address this, we introduce a dual-memory augmented HMR critique agent with self-reflection to produce context-aware quality scores for predicted meshes. These scores distill fine-grained cues about 3D human motion structure, physical feasibility, and alignment with the input image. We use these scores to build a group-wise HMR preference dataset. Leveraging this dataset, we propose a group preference alignment framework for finetuning diffusion-based HMR models. This process injects the rich preference signals into the model, guiding it to generate more physically plausible and image-consistent human meshes. Extensive experiments demonstrate that our method achieves superior performance compared to state-of-the-art approaches.

Wenhao Shen, Hao Wang, Wanqi Yin +5

Nanyang Technological University · HKUST(GZ) · SenseTime Research +1

Human Mesh Recovery 3D Human Reconstruction Diffusion Model Alignment Diffusion Models Preference Optimization

Feb 21, 2026

Insertion Based Sequence Generation with Learnable Order Dynamics

Existing insertion-based masked diffusion models that generate sequences by interleaving token insertion with unmasking use fixed schedules that are not dependent on the data. For structured sequences like graphs and molecules, learning data-dependent generation orders can improve generation quality by reducing uncertainty over the action space. We propose LoFlexMDM, an insertion-based masked diffusion model with learnable order dynamics that learns data-dependent insertion and unmasking rates. We generalize the discrete flow matching framework to work with variable-length sequences, propose a tractable schedule parameterization and a training objective for joint training of the generator and the target order dynamics. On De Novo and fragment-constrained molecule generation, LoFlexMDM improves sample quality over FlexMDM by up to 17.5% and 6.7%, respectively. These results show that learning the target generation order can improve insertion-based diffusion models without giving up tractable training. We open source the code at https://github.com/dhruvdcoder/LoFlexMDM.

Dhruvesh Patel, Benjamin Rozonoyer, Gaurav Pandey +3

University of Massachusetts Amherst · IBM Research

Diffusion Models Masked Diffusion Models Molecular Graph Generation Discrete Flow Matching

Feb 20, 2026

The Geometry of Noise: Why Diffusion Models Don't Need Noise Conditioning

Autonomous (noise-agnostic) generative models, such as Equilibrium Matching and blind diffusion, challenge the standard paradigm by learning a single, time-invariant vector field that operates without explicit noise-level conditioning. While recent work suggests that high-dimensional concentration allows these models to implicitly estimate noise levels from corrupted observations, a fundamental paradox remains: what is the underlying landscape being optimized when the noise level is treated as a random variable, and how can a bounded, noise-agnostic network remain stable near the data manifold where gradients typically diverge? We resolve this paradox by formalizing Marginal Energy,

E_{\text{marg}}(\mathbf{u}) = -\log p(\mathbf{u})

, where

p(\mathbf{u}) = \int p(\mathbf{u}|t)p(t)dt

is the marginal density of the noisy data integrated over a prior distribution of unknown noise levels. We prove that generation using autonomous models is not merely blind denoising, but a specific form of Riemannian gradient flow on this Marginal Energy. Through a novel relative energy decomposition, we demonstrate that while the raw Marginal Energy landscape possesses a

1/t^p

singularity normal to the data manifold, the learned time-invariant field implicitly incorporates a local conformal metric that perfectly counteracts the geometric singularity, converting an infinitely deep potential well into a stable attractor. We also establish the structural stability conditions for sampling with autonomous models. We identify a ``Jensen Gap'' in noise-prediction parameterizations that acts as a high-gain amplifier for estimation errors, explaining the catastrophic failure observed in deterministic blind models. Conversely, we prove that velocity-based parameterizations are inherently stable because they satisfy a bounded-gain condition that absorbs posterior uncertainty into a smooth geometric drift.

Mojtaba Sahraee-Ardakan, Mauricio Delbracio, Peyman Milanfar

Google

Diffusion Models Diffusion Sampling

Feb 20, 2026

Annealed Co-Generation: Disentangling Variables via Progressive Pairwise Modeling

For multivariate co-generation in scientific applications, we advocate pairwise block rather than joint modeling of all variables. This design mitigates the computational burden and data imbalance. To this end, we propose an Annealed Co-Generation (ACG) framework that replaces high-dimensional diffusion modeling with a low-dimensional diffusion model, which enables multivariate co-generation by composing pairwise variable generations. We first train an unconditional diffusion model over causal variables that are disentangled into pairs. At inference time, we recover the joint distribution by coupling these pairwise models through shared common variables, enabling coherent multivariate generation without any additional training. By employing a three-stage annealing process-Consensus, Heating, and Cooling-our method enforces consistency across shared common variables and progressively constrains each pairwise data distribution to lie on a learnable manifold, while maintaining high likelihood within each pair. We demonstrate the framework's flexibility and efficacy on two distinct scientific tasks: flow-field completion and antibody generation. All datasets and code will be made publicly available upon publication.

Hantao Zhang, Jieke Wu, Mingda Xu +3

CVLab, EPFL

Generative Modeling Diffusion Models Constrained Generative Modeling

Feb 20, 2026

Correlation Analysis of Generative Models

Based on literature review about existing diffusion models and flow matching with a neural network to predict a predefined target from noisy data, a unified representation is first proposed for these models using two simple linear equations in this paper. Theoretical analysis of the proposed model is then presented. Our theoretical analysis shows that the correlation between the noisy data and the predicted target is sometimes weak in the existing diffusion models and flow matching. This might affect the prediction (or learning) process which plays a crucial role in all models.

Zhengguo Li, Chaobing Zheng, Wei Wang

VI Department, Institute for Infocomm Research, A*STAR, Singapore, 138632 · School of ISE, Wuhan University of Science and Technology, Wuhan, China · School of CST, Wuhan University of Science and Technology, Wuhan, China

Generative Modeling Diffusion Models Flow Matching

Feb 19, 2026

Two Calm Ends and the Wild Middle: A Geometric Picture of Memorization in Diffusion Models

Diffusion models generate high-quality samples but can also memorize training data, raising serious privacy concerns. Understanding the mechanisms governing when memorization versus generalization occurs remains an active area of research. In particular, it is unclear where along the noise schedule memorization is induced, how data geometry influences it, and how phenomena at different noise scales interact. We introduce a geometric framework that partitions the noise schedule into three regimes based on the coverage properties of training data by Gaussian shells and the concentration behavior of the posterior, which we argue are two fundamental objects governing memorization and generalization in diffusion models. This perspective reveals that memorization risk is highly non-uniform across noise levels. We further identify a danger zone at medium noise levels where memorization is most pronounced. In contrast, both the small and large noise regimes resist memorization, but through fundamentally different mechanisms: small noise avoids memorization due to limited training coverage, while large noise exhibits low posterior concentration and admits a provably near linear Gaussian denoising behavior. For the medium noise regime, we identify geometric conditions through which we propose a geometry-informed targeted intervention that mitigates memorization.

Nick Dodson, Xinyu Gao, Qingsong Wang +2

Department of Mathematics, University of Missouri, Columbia, Missouri, USA · Halıcıo˘glu Data Science Institute, University of California San Diego, La Jolla, California, USA

Memorization in Generative Models Diffusion Models

Feb 19, 2026

MolHIT: Advancing Molecular-Graph Generation with Hierarchical Discrete Diffusion Models

Molecular generation with diffusion models has emerged as a promising direction for AI-driven drug discovery and materials science. While graph diffusion models have been widely adopted due to the discrete nature of 2D molecular graphs, existing models suffer from low chemical validity and struggle to meet the desired properties compared to 1D modeling. In this work, we introduce MolHIT, a powerful molecular graph generation framework that overcomes long-standing performance limitations in existing methods. MolHIT is based on the Hierarchical Discrete Diffusion Model, which generalizes discrete diffusion to additional categories that encode chemical priors, and decoupled atom encoding that splits the atom types according to their chemical roles. Overall, MolHIT achieves new state-of-the-art performance on the MOSES dataset with near-perfect validity for the first time in graph diffusion, surpassing strong 1D baselines across multiple metrics. We further demonstrate strong performance in downstream tasks, including multi-property guided generation and scaffold extension.

Hojung Jung, Rodrigo Hormazabal, Jaehyeong Jo +5

KAIST AI · LG AI Research · Seoul National University

Molecular Graph Generation Diffusion Models Graph Diffusion

Feb 19, 2026

Unified Latents (UL): How to train your latents

We present Unified Latents (UL), a framework for learning latent representations that are jointly regularized by a diffusion prior and decoded by a diffusion model. By linking the encoder's output noise to the prior's minimum noise level, we obtain a simple training objective that provides a tight upper bound on the latent bitrate. On ImageNet-512, our approach achieves competitive FID of 1.4, with high reconstruction quality (PSNR) while requiring fewer training FLOPs than models trained on Stable Diffusion latents. On Kinetics-600, we set a new state-of-the-art FVD of 1.3.

Jonathan Heek, Emiel Hoogeboom, Thomas Mensink +1

Google DeepMind Amsterdam

Diffusion Autoencoder Latent Diffusion Models Representation Learning Diffusion Models Diffusion-Based Image Generation Video Diffusion Models

Feb 18, 2026

Unpaired Image-to-Image Translation via a Self-Supervised Semantic Bridge

Adversarial diffusion and diffusion-inversion methods have advanced unpaired image-to-image translation, but each faces key limitations. Adversarial approaches require target-domain adversarial loss during training, which can limit generalization to unseen data, while diffusion-inversion methods often produce low-fidelity translations due to imperfect inversion into noise-latent representations. In this work, we propose the Self-Supervised Semantic Bridge (SSB), a versatile framework that integrates external semantic priors into diffusion bridge models to enable spatially faithful translation without cross-domain supervision. Our key idea is to leverage self-supervised visual encoders to learn representations that are invariant to appearance changes but capture geometric structure, forming a shared latent space that conditions the diffusion bridges. Extensive experiments show that SSB outperforms strong prior methods for challenging medical image synthesis in both in-domain and out-of-domain settings, and extends easily to high-quality text-guided editing.

Jiaming Liu, Felix Petersen, Yunhe Gao +6

Stanford University · LLNL · Johns Hopkins University

Unpaired Image-to-Image Translation Diffusion Models Medical Image Synthesis

Feb 18, 2026

Quantifying Error Propagation and Model Collapse in Diffusion Models

Machine learning models are increasingly trained or fine-tuned on synthetic data. Recursively training on such data has been observed to significantly degrade performance in a wide range of tasks, often characterized by a progressive drift away from the target distribution. In this work, we theoretically analyze this phenomenon in the setting of score-based diffusion models. For a realistic pipeline where each training round uses a combination of synthetic data and fresh samples from the target distribution, we obtain upper and lower bounds on the accumulated divergence between the generated and target distributions. Notably, to the best of our knowledge, this is the first lower bound on the divergence between the learned and target distributions, even for standard diffusion models. Our results allow us to characterize different regimes of drift, depending on the score estimation error and the proportion of fresh data used in each generation. In a certain regime, the accumulated divergence after several retraining rounds can be expressed as a discounted sum of score estimation errors made at each generation. We also provide empirical results on synthetic data and images to illustrate the theory.

Nail B. Khelifa, Richard E. Turner, Ramji Venkataramanan

University of Cambridge, Cambridge, United Kingdom.

Model Collapse Diffusion Models Score-Based Generative Modeling

Feb 18, 2026

Steering diffusion models with quadratic rewards: a fine-grained analysis

Inference-time algorithms are an emerging paradigm in which pre-trained models are used as subroutines to solve downstream tasks. Such algorithms have been proposed for tasks ranging from inverse problems and guided image generation to reasoning. However, the methods currently deployed in practice are heuristics with a variety of failure modes -- and we have very little understanding of when these heuristics can be efficiently improved. In this paper, we consider the task of sampling from a reward-tilted diffusion model -- that is, sampling from

p^{\star}(x) \propto p(x) \exp(r(x))

-- given a reward function

r

and pre-trained diffusion oracle for

p

. We provide a fine-grained analysis of the computational tractability of this task for quadratic rewards

r(x) = x^\top A x + b^\top x

. We show that linear-reward tilts are always efficiently sampleable -- a simple result that seems to have gone unnoticed in the literature. We use this as a building block, along with a conceptually new ingredient -- the Hubbard-Stratonovich transform -- to provide an efficient algorithm for sampling from low-rank positive-definite quadratic tilts, i.e.

r(x) = x^\top A x

where

A

is positive-definite and of rank

O(1)

. For negative-definite tilts, i.e.

r(x) = - x^\top A x

where

A

is positive-definite, we prove that the problem is intractable even if

A

is of rank 1 (albeit with exponentially-large entries).

Ankur Moitra, Andrej Risteski, Dhruv Rohatgi

Diffusion Sampling Diffusion Models Inference-Time Guidance

Feb 18, 2026

Fast and Scalable Analytical Diffusion

Analytical diffusion models offer a mathematically transparent path to generative modeling by formulating the denoising score as an empirical-Bayes posterior mean. However, this interpretability comes at a prohibitive cost: the standard formulation necessitates a full-dataset scan at every timestep, scaling linearly with dataset size. In this work, we present the first systematic study addressing this scalability bottleneck. We challenge the prevailing assumption that the entire training data is necessary, uncovering the phenomenon of Posterior Progressive Concentration: the effective golden support of the denoising score is not static but shrinks asymptotically from the global manifold to a local neighborhood as the signal-to-noise ratio increases. Capitalizing on this, we propose Dynamic Time-Aware Golden Subset Diffusion (GoldDiff), a training-free framework that decouples inference complexity from dataset size. Instead of static retrieval, GoldDiff uses a coarse-to-fine mechanism to dynamically pinpoint the ''Golden Subset'' for inference. Theoretically, we derive rigorous bounds guaranteeing that our sparse approximation converges to the exact score. Empirically, GoldDiff achieves a

\bf 71 \times

speedup on AFHQ while matching or achieving even better performance than full-scan baselines. Most notably, we demonstrate the first successful scaling of analytical diffusion to ImageNet-1K, unlocking a scalable, training-free paradigm for large-scale generative modeling.

Xinyi Shang, Peng Sun, Jingyu Lin +1

University College London · Mohamed bin Zayed University of Artificial Intelligence · Zhejiang University +2

Diffusion Models Diffusion Model Inference Acceleration Diffusion Sampling

Feb 18, 2026

Training-Free Adaptation of Diffusion Models via Doob's $h$ -Transform

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.

Qijie Zhu, Zeqi Ye, Han Liu +2

Department of Statistics and Data Science, Northwestern University. · Department of Industrial Engineering and Management Sciences, Northwestern University. · Department of Computer Science, Northwestern University.

Diffusion Model Adaptation Diffusion Models Diffusion Model Guidance Diffusion Sampling RL for Diffusion Models Doob H-Transform

Feb 17, 2026

GlobeDiff: State Diffusion Process for Partial Observability in Multi-Agent Systems

In the realm of multi-agent systems, the challenge of partial observability is a critical barrier to effective coordination and decision-making. Existing approaches, such as belief state estimation and inter-agent communication, often fall short. Belief-based methods are limited by their focus on past experiences without fully leveraging global information, while communication methods often lack a robust model to effectively utilize the auxiliary information they provide. To solve this issue, we propose Global State Diffusion Algorithm~(GlobeDiff) to infer the global state based on the local observations. By formulating the state inference process as a multi-modal diffusion process, GlobeDiff overcomes ambiguities in state estimation while simultaneously inferring the global state with high fidelity. We prove that the estimation error of GlobeDiff under both unimodal and multi-modal distributions can be bounded. Extensive experimental results demonstrate that GlobeDiff achieves superior performance and is capable of accurately inferring the global state.

Yiqin Yang, Xu Yang, Yuhua Jiang +8

The Key Laboratory of Cognition and Decision Intelligence for Complex Systems, Institute of Automation, Chinese Academy of Sciences · Tsinghua University · Moonshot AI +2

Multi-Agent Systems Diffusion Models

Feb 17, 2026

Joint Enhancement and Classification using Coupled Diffusion Models of Signals and Logits

Robust classification in noisy environments remains a fundamental challenge in machine learning. Standard approaches typically treat signal enhancement and classification as separate, sequential stages: first enhancing the signal and then applying a classifier. This approach fails to leverage the semantic information in the classifier's output during denoising. In this work, we propose a general, domain-agnostic framework that integrates two interacting diffusion models: one operating on the input signal and the other on the classifier's output logits, without requiring any retraining or fine-tuning of the classifier. This coupled formulation enables mutual guidance, where the enhancing signal refines the class estimation and, conversely, the evolving class logits guide the signal reconstruction towards discriminative regions of the manifold. We introduce three strategies to effectively model the joint distribution of the input and the logit. We evaluated our joint enhancement method for image classification and automatic speech recognition. The proposed framework surpasses traditional sequential enhancement baselines, delivering robust and flexible improvements in classification accuracy under diverse noise conditions.

Gilad Nurko, Roi Benita, Yehoshua Dissen +4

Technion – Israel Institute of Technology, Haifa, Israel · NTT, Inc., Japan.

Robust Classification Diffusion Models Diffusion Model Guidance Image Classification Automatic Speech Recognition

Feb 17, 2026

Efficient Generative Modeling beyond Memoryless Diffusion via Adjoint Schrödinger Bridge Matching

Diffusion models often yield highly curved trajectories and noisy score targets due to an uninformative, memoryless forward process that induces independent data-noise coupling. We propose Adjoint Schrödinger Bridge Matching (ASBM), a generative modeling framework that recovers optimal trajectories in high dimensions via two stages. First, we view the Schrödinger Bridge (SB) forward dynamic as a coupling construction problem and learn it through a data-to-energy sampling perspective that transports data to an energy-defined prior. Then, we learn the backward generative dynamic with a simple matching loss supervised by the induced optimal coupling. By operating in a non-memoryless regime, ASBM produces significantly straighter and more efficient sampling paths. Compared to prior works, ASBM scales to high-dimensional data with notably improved stability and efficiency. Extensive experiments on image generation show that ASBM improves fidelity with fewer sampling steps. We further showcase the effectiveness of our optimal trajectory via distillation to a one-step generator.

Jeongwoo Shin, Jinhwan Sul, Joonseok Lee +2

Seoul National University, Seoul, Korea · Georgia Institute of Technology, Atlanta, GA, USA · Sungkyunkwan University, Seoul, Korea

Diffusion Model Sampling Schrödinger Bridges Few-Step Diffusion Sampling Diffusion Models

Feb 17, 2026

Steering Dynamical Regimes of Diffusion Models by Breaking Detailed Balance

We show that deliberately breaking detailed balance in generative diffusion processes can accelerate the reverse process without changing the stationary distribution. Considering the Ornstein--Uhlenbeck process, we decompose the dynamics into a symmetric component and a non-reversible anti-symmetric component that generates rotational probability currents. We then construct an exponentially optimal non-reversible perturbation that improves the long-time relaxation rate while preserving the stationary target. We analyze how such non-reversible control reshapes the macroscopic dynamical regimes of the phase transitions recently identified in generative diffusion models. We derive a general criterion for the speciation time and show that suitable non-reversible perturbations can accelerate speciation. In contrast, the collapse transition is governed by a trace-controlled phase-space contraction mechanism that is fixed by the symmetric component, and the corresponding collapse time remains unchanged under anti-symmetric perturbations. Numerical experiments on Gaussian mixture models support these findings.

Haiqi Lu, Ying Tang

Institute of Fundamental and Frontier Sciences, University of Electronic Science and Technology of China, Chengdu 611731, China · Yingcai Honor College, University of Electronic Science and Technology of China, Chengdu 611731, China · School of Physics, University of Electronic Science and Technology of China, Chengdu 611731, China +2

Diffusion Models Diffusion Sampling Diffusion Model Acceleration Stochastic Differential Equations

Feb 16, 2026

Rethinking Diffusion Models with Symmetries through Canonicalization with Applications to Molecular Graph Generation

Many generative tasks in chemistry and science involve distributions invariant to group symmetries (e.g., permutation and rotation). A common strategy enforces invariance and equivariance through architectural constraints such as equivariant denoisers and invariant priors. In this paper, we challenge this tradition through the alternative canonicalization perspective: first map each sample to an orbit representative with a canonical pose or order, train an unconstrained (non-equivariant) diffusion or flow model on the canonical slice, and finally recover the invariant distribution by sampling a random symmetry transform at generation time. Building on a formal quotient-space perspective, our work provides a comprehensive theory of canonical diffusion by proving: (i) the correctness, universality and superior expressivity of canonical generative models over invariant targets; (ii) canonicalization accelerates training by removing diffusion score complexity induced by group mixtures and reducing conditional variance in flow matching. We then show that aligned priors and optimal transport act complementarily with canonicalization and further improves training efficiency. We instantiate the framework for molecular graph generation under

S_n \times SE(3)

symmetries. By leveraging geometric spectra-based canonicalization and mild positional encodings, canonical diffusion significantly outperforms equivariant baselines in 3D molecule generation tasks, with similar or even less computation. Moreover, with a novel architecture Canon, CanonFlow achieves state-of-the-art performance on the challenging GEOM-DRUG dataset, and the advantage remains large in few-step generation.

Cai Zhou, Zijie Chen, Zian Li +7

Massachusetts Institute of Technology · Zhejiang University · Peking University +3

Generative Modeling Diffusion Models 3D Molecular Generation Molecular Graph Generation Flow-Based Generative Modeling

Feb 16, 2026

Scaling Beyond Masked Diffusion Language Models

Diffusion language models are a promising alternative to autoregressive models due to their potential for faster generation. Among discrete diffusion approaches, Masked diffusion currently dominates, largely driven by strong perplexity on language modeling benchmarks. In this work, we present the first scaling law study of uniform-state and interpolating discrete diffusion methods. We also show that Masked diffusion models can be made approximately 12% more FLOPs-efficient when trained with a simple cross-entropy objective. We find that perplexity is informative within a diffusion family but can be misleading across families, where models with worse likelihood scaling may be preferable due to faster and more practical sampling, as reflected by the speed-quality Pareto frontier. These results challenge the view that Masked diffusion is categorically the future of diffusion language modeling and that perplexity alone suffices for cross-algorithm comparison. Scaling all methods to 1.7B parameters, we show that uniform-state diffusion remains competitive on likelihood-based benchmarks and outperforms autoregressive and Masked diffusion models on GSM8K, despite worse validation perplexity. We provide the code, model checkpoints, and video tutorials on the project page: http://s-sahoo.github.io/scaling-dllms

Subham Sekhar Sahoo, Jean-Marie Lemercier, Zhihan Yang +4

NVIDIA, Santa Clara, USA · Department of Computer Science, Cornell Tech, NYC, USA · Department of Computer Science, Cornell University, Ithaca, USA +2

Diffusion Language Models Diffusion Models Diffusion Language Model Training Diffusion Language Model Benchmarking Masked Diffusion Models Diffusion Language Model Inference

Feb 16, 2026

Efficient Sampling with Discrete Diffusion Models: Sharp and Adaptive Guarantees

Diffusion models over discrete spaces have recently shown striking empirical success, yet their theoretical foundations remain incomplete. In this paper, we study the sampling efficiency of score-based discrete diffusion models under a continuous-time Markov chain (CTMC) formulation, with a focus on

τ

-leaping-based samplers. We establish sharp convergence guarantees for attaining

\varepsilon

accuracy in Kullback-Leibler (KL) divergence for both uniform and masking noising processes. For uniform discrete diffusion, we show that the

τ

-leaping algorithm achieves an iteration complexity of order

\tilde O(d/\varepsilon)

, with

d

the ambient dimension of the target distribution, eliminating linear dependence on the vocabulary size

S

and improving existing bounds by a factor of

d

; moreover, we establish a matching algorithmic lower bound showing that linear dependence on the ambient dimension is unavoidable in general. For masking discrete diffusion, we introduce a modified

τ

-leaping sampler whose convergence rate is governed by an intrinsic information-theoretic quantity, termed the effective total correlation, which is bounded by

d \log S

but can be sublinear or even constant for structured data. As a consequence, the sampler provably adapts to low-dimensional structure without prior knowledge or algorithmic modification, yielding sublinear convergence rates for various practical examples (such as hidden Markov models, image data, and random graphs). Our analysis requires no boundedness or smoothness assumptions on the score estimator beyond control of the score entropy loss.

Daniil Dmitriev, Zhihan Huang, Yuting Wei

Department of Statistics and Data Science, the Wharton School, University of Pennsylvania

Sample Complexity Diffusion Model Sampling Diffusion Sampling Diffusion Models

Feb 13, 2026

High-Resolution Climate Projections Using Diffusion-Based Downscaling of a Lightweight Climate Emulator

The proliferation of data-driven models in weather and climate sciences has marked a significant paradigm shift, with advanced models demonstrating exceptional skill in medium-range forecasting. However, these models are often limited by long-term instabilities, climatological drift, and substantial computational costs during training and inference, restricting their broader application for climate studies. Addressing these limitations, Guan et al. (2024) introduced LUCIE, a lightweight, physically consistent climate emulator utilizing a Spherical Fourier Neural Operator (SFNO) architecture. This model is able to reproduce accurate long-term statistics including climatological mean and seasonal variability. However, LUCIE's native resolution (~300 km) is inadequate for detailed regional impact assessments. To overcome this limitation, we introduce a deep learning-based downscaling framework, leveraging probabilistic diffusion-based generative models with conditional and posterior sampling frameworks. These models downscale coarse LUCIE outputs to 25 km resolution. They are trained on approximately 14,000 ERA5 timesteps spanning 2000-2009 and evaluated on LUCIE predictions from 2010 to 2020. Model performance is assessed through diverse metrics, including latitude-averaged RMSE, power spectrum, probability density functions and First Empirical Orthogonal Function of the zonal wind. We observe that the proposed approach is able to preserve the coarse-grained dynamics from LUCIE while generating fine-scaled climatological statistics at ~28km resolution.

Haiwen Guan, Dibyajyoti Chakraborty, Moein Darman +3

1Information Sciences and Technology, The Pennsylvania State University, University Park, Pennsylvania · Department of Applied Mathematics, University of California, Santa Cruz, California · 3Allen Institute for Artificial Intelligence (AI2), Seattle, Washington +1

Climate Science Climate Modeling Conditional Diffusion Models Climate Downscaling Diffusion Models

Feb 10, 2026

ELROND: Exploring and decomposing intrinsic capabilities of diffusion models

A single text prompt passed to a diffusion model yields a wide range of visual outputs determined solely by a stochastic process, leaving users with no direct control over which semantic variations appear. Exploring this range is difficult: random search offers no guarantee of covering it, while prompt editing is coarse, as even a small change in wording can substantially alter the generated image. We argue that systematic exploration instead requires recovering how the model itself organizes the conditional distributions it can produce. We formalize this structure as a generative manifold, and present ELROND, a method for recovering its tangent space at a given conditioning. To that end, we collect gradients obtained by backpropagating the differences between stochastic realizations of a fixed prompt, and decompose them into interpretable directions using Principal Component Analysis or a Sparse Autoencoder. We show that our method recovers this subspace accurately in a controlled setting and validate it behaviorally on large-scale models. We also demonstrate that recovered structure enables broader exploration of the model's capabilities than methods relying on external representations, and mitigates mode collapse in distilled models without retraining.

Paweł Skierś, Emilia Kaczmarczyk, Tomasz Trzciński +1

Warsaw University of Technology · IDEAS Research Institute

Diffusion Models T2I Diffusion Models

Feb 6, 2026

Improved Sampling Schedules for Discrete Diffusion Models

Uniform Discrete Diffusion Models have emerged as a powerful paradigm for generative modeling on sequence data; however, the information-theoretic principles governing their reverse processes remain underexplored. In this work, we bridge this gap by analyzing the reverse process dynamics through the lens of thermodynamic entropy production and dynamical activity. We use a variational expression of the discrete Wasserstein distance to characterize the dynamics of the generation process. Leveraging these insights, we first introduce the Entropic Discrete Schedule (EDS), which aligns with entropy production, and later construct the Wasserstein Discrete Schedule (WDS), which combines entropy production and dynamical activity to act as a geometric cost. Our experimental results on language modeling show that WDS provide the same results as uniform while using up to half of the computations on the MBPP benchmark. The code is available at https://github.com/AlbertoForesti/impscheds.

Alberto Foresti, Mustapha Bounoua, Giulio Franzese +2

Department of Data Science, EURECOM, 450 Route des Chappes, 06410 Biot, France · Donders Institute for Brain, Cognition and Behaviour, Radboud University, Postbus 9102, 6500 HC Nijmegen, Netherlands

Diffusion Sampling Diffusion Models Diffusion Timestep Scheduling

Feb 4, 2026

Rethinking the Design Space of Reinforcement Learning for Diffusion Models: On the Importance of Likelihood Estimation Beyond Loss Design

Reinforcement learning has been widely applied to diffusion and flow models for visual tasks such as text-to-image generation. However, these tasks remain challenging because diffusion models have intractable likelihoods, which creates a barrier for directly applying popular policy-gradient type methods. Existing approaches primarily focus on crafting new objectives built on already heavily engineered LLM objectives, using ad hoc estimators for likelihood, without a thorough investigation into how such estimation affects overall algorithmic performance. In this work, we provide a systematic analysis of the RL design space by disentangling three factors: i) policy-gradient objectives, ii) likelihood estimators, and iii) rollout sampling schemes. We show that adopting an evidence lower bound (ELBO) based model likelihood estimator, computed only from the final generated sample, is the dominant factor enabling effective, efficient, and stable RL optimization, outweighing the impact of the specific policy-gradient loss functional. We validate our findings across multiple reward benchmarks using SD 3.5 Medium, and observe consistent trends across all tasks. Our method improves the GenEval score from 0.24 to 0.95 in 90 GPU hours, which is 4.6 times more efficient than FlowGRPO and

2\times

more efficient than the SOTA method without reward hacking.

Jaemoo Choi, Yuchen Zhu, Wei Guo +6

Georgia Institute of Technology · National University of Singapore · Nanjing university.

T2I Generation Diffusion Model Fine-Tuning Policy Gradient Methods RL for Diffusion Models Diffusion Models