Flow Matching

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79 papers in the last four weeks, up 365% on the four weeks before. 0.8% of all new papers.

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Latest papers 446

Aug 4, 2026cs.CV

Residual Flow Matching with Dynamic Cross-Interaction for 3D Multi-Person Motion Prediction

3D multi-person motion prediction requires modeling both individual kinematics and inter-person interactions. While Flow Matching is effective for multi-hypothesis generation to improve prediction accuracy, directly predicting skeletal sequences from pure noise often compromises structural consistency and introduces unreliable cross-agent interactions during early noise-dominated integration steps. To address this, we propose a Prior-Guided Residual Flow Matching framework. First, a Deterministic Coarse Prior (DCP) establishes a kinematic anchor, formulating the generative process as a conditional flow over motion residuals to simplify the generative objective and preserve structural stability. Second, a Dynamic Cross-Interaction (DCI) mechanism temporally synchronizes inter-agent message-passing with the integration progress, ensuring the extraction of reliable social contexts and improving multi-person motion fidelity. Finally, a decoupled joint-motion architecture with bidirectional fusion effectively preserves fine-grained kinematic coherence. Extensive experiments demonstrate that our approach achieves state-of-the-art prediction accuracy across multiple datasets. Code is available at https://github.com/Wei-Wei-a/Residual-Flow-Matching-with-Dynamic-Cross-Interaction-for-3D-Multi-Person-Motion-Prediction.

Wei Wei, Yinyuan Zhao, Ruixuan Yu

Shandong University

Flow Matching Human Motion Prediction

Aug 4, 2026cs.LG

Any-OPD: Heterogeneous On-Policy Distillation for Flow-Matching Models via Representation-Space Bridging

On-policy distillation, in which a teacher corrects samples that the student itself generates, presupposes that the two models speak the same language: identical VAE latents, matching architectures, and a common timestep grid. We ask what happens when none of this holds, as when the strongest teacher available and the student one wishes to deploy come from different model families, and find that the standard recipes have no answer: teacher latents cannot serve as targets in a foreign coordinate system, per-pixel losses against a teacher that stochastically re-draws local detail degenerate into blur or divergence, and timestep indices lose their meaning across mismatched schedules. We present Any-OPD, to our knowledge the first framework for on-policy distillation between arbitrary pairs of latent flow-matching generators. Any-OPD treats the teacher purely as a black-box sampler and connects the two models at exactly one point: a frozen, model-agnostic vision representation in which their independently decoded outputs are compared, sidestepping every assumption about latents, features, or architecture. Trajectory correspondence is recovered by matching continuous noise levels instead of step indices, and a brief anchoring phase, in which teacher samples are re-encoded through the student's own VAE, ensures the on-policy gradient measures sample quality rather than domain mismatch. Distilling the 12B FLUX.1-dev into the 2.5B SD3.5-Medium, Any-OPD lifts the student's PickScore from 0.846 to 0.884 and HPSv3 from 9.12 to 10.97, rivaling the teacher at a fifth of its size, where direct latent regression fails to train at all.

Siming Fu, Zheming Fu, Ruizhe He +7

1Joy Future Academy · 2Zhejiang University

Flow Matching Diffusion Model Distillation T2I Generation Cross-Architecture Knowledge Distillation On-Policy Distillation

Aug 4, 2026cs.RO

GraspMeanFlow: SE(3)-Equivariant MeanFlow for Few-Step 6-DoF Grasp Generation

Recent data-driven methods for synthesizing 6-DoF grasp poses use generative models to learn complex grasp pose distributions and generate diverse candidate poses. In particular, SE(3)-equivariant flow-based models generate grasp poses that transform consistently with object rotations and translations. However, these methods sample by iterative numerical integration, requiring tens of function evaluations per grasp and limiting their use in real-time manipulation. We propose GraspMeanFlow, an SE(3)-equivariant MeanFlow framework for few-step 6-DoF grasp generation. Our method learns the average velocity over a finite time interval, defined through the time-ordered exponential so that it reproduces exactly the rigid-body displacement accumulated over that interval. We prove that a point-cloud-conditioned distribution transported by an equivariant average-velocity flow map remains invariant, so equivariance is retained under few-step sampling, and we condition the field on a pair of times by lifting both to equivariant vectors, leaving the backbone otherwise unchanged. For stable training, we pair a flow-matching boundary term with either of two consistency terms: the differential MeanFlow identity, whose target requires a Jacobian-vector product, or an equivalent semigroup loss that avoids it. Experiments on ACRONYM show that a single function evaluation of GraspMeanFlow reaches the EMD that an iterative SE(3) flow model needs five steps to approach, that a second instantiation of the same framework improves grasp success by up to 24.3 points in the few-step regime, and that both generate grasp distributions transforming exactly with the object.

Jiyong Kwon, Yikun Bai, Amirhossein Mollaali +1

School of Mechanical Engineering, Purdue University · Department of Mathematics, Purdue University

Flow Matching Robotic Grasping Equivariant Neural Networks Mean Flow

Aug 4, 2026cs.RO

PFM-HR: Pose Flow Matching for Humanoid Robots

Motion priors improve reinforcement learning for physics-based humanoid tracking, but temporal priors require ordered motion clips, while pose priors provide limited guidance for policy-induced pose transitions. We present Pose Flow Matching for Humanoid Robots (PFM-HR), a reusable flow matching prior trained directly on large scale unordered pose data. PFM-HR introduces the Pose Geometry Score (PGS), which quantifies how joint coordinate changes during rollouts align with the local geometry of pose variation captured by the prior. Using PGS to modulate the tracking reward guides policy exploration toward structured pose changes while keeping the prior frozen across tracking tasks. Experiments demonstrate that PFM-HR improves both single motion and general motion tracking, especially for highly dynamic motions.

Yukang Gao, Yi Gu, Yangchen Zhou +9

1HKUST(GZ) · 2Noitom Robotics · 4Google +1

RL for Robotics Flow Matching Reinforcement Learning Humanoid Motion Tracking

Aug 4, 2026eess.AS

GROW: Group-Relative Advantage-Weighted On-Policy Reinforcement Learning of Autoregressive-Diffusion Text-to-Speech model

Reinforcement learning for flow-matching text-to-speech is complicated by deterministic ODE sampling: trajectory-level policy-gradient methods typically convert the ODE into an SDE and track per-step likelihood ratios, introducing stochastic perturbations and substantial overhead. We propose GROW, a group-relative advantage-weighted on-policy RL method that acts directly on the standard flow-matching objective. For each prompt, GROW samples a group of on-policy utterances, separately standardizes intelligibility and speaker-similarity rewards within the group, and combines them to reweight flow-matching regression. A Wasserstein-2 velocity penalty anchors the updated model to a frozen pretrained reference. A group-mean reward baseline is introduced to convert reward weighting into advantage weighting. For strong pretrained TTS models with concentrated rewards, positive exponential weighting is dominated by reward-agnostic self-imitation, whereas a zero-mean signed advantage preserves effective within-group credit assignment. Instantiated on DiTAR and evaluated on LibriSpeech and Seed-TTS EN/ZH, GROW reduces average WER from 2.016 to 1.558 and raises speaker similarity from 0.676 to 0.715 while keeping UTMOS. With 10-NFE training rollouts and 32-NFE evaluation, GROW retains comparable performance while training 2.9x faster than 32-NFE DiTAR-GRPO. We will open-source complete GROW codes, faithful DiTAR reproduction, and all model checkpoints.

Guanrou Yang, Tian Tan, Qian Chen +8

Shanghai Jiao Tong University · Shanghai Innovation Institute · Independent Researcher +2

Flow Matching TTS Synthesis Audio Diffusion Models RL for Generative Models

Aug 3, 2026cs.CV

SPARE: Structural Parameter-Free Affinity Regularization for Flow Matching

Denoising diffusion transformers achieve strong generation quality but converge slowly during training. Regularizing their internal representations has emerged as an effective accelerator, yet existing methods split into two families with complementary costs. Target-based methods strengthen representations by aligning them to external features, which requires an external encoder and a learnable projection head to bridge feature spaces. Target-free methods hold no reference at all, and can only repel the model's own features across samples or layers, discarding whatever structure the data contains. Prior work suggests that spatial structure, rather than global semantics, drives the gains of alignment. We therefore ask whether such structure can serve as a target directly, and whether it exists not only within an image but across images. Our key insight is that the clean data latent already carries this structure in the relations among its tokens, where a relation is the similarity between two tokens, a single scalar comparable across feature spaces without a projection head. We propose Structural Parameter-free Affinity Regularization (SPARE), a regularizer that matches the pairwise affinities of intermediate tokens to those of the clean latents. To exploit this structure fully, SPARE extends the matching to token pairs across images, precisely the pairs that prior target-free methods repel by default, and calibrates both relation types with a single learning objective. On ImageNet

256 \times 256

with SiT backbones under matched 400K-iteration budgets, SPARE adds no encoder, head, or parameters and only 0.08 GB of training memory, yet attains the lowest FID among parameter-free regularizers in every tested setting, recovers 37 to 54% of REPA's FID reduction, and improves over REPA when combined with it, reaching FID 1.90 under classifier-free guidance at 1M iterations.

Zong-Wei Hong, Jinglun Li, Shen Zhang +3

JIIOV Technology

Diffusion Model Alignment Flow Matching Representation Learning Diffusion Transformer Diffusion-Based Image Generation

Aug 3, 2026cs.LG

Beckmann Transport Models: From Autonomous Flows to One-Step Maps

We propose an instantiation of flow matching that relies on a time-independent velocity field (an \emph{autonomous flow}) to exactly map between two distributions, so long as the target is singular, i.e.\ supported on a lower-dimensional data manifold. We also show that the one-step generative map associated with this flow is the unique solution of a simple conservation equation, which can be used to learn the map directly from samples. These autonomous flows and maps give a dynamical meaning to the flux constraint of Beckmann's transportation problem. Their construction provides a unifying framework that recovers, for instance, the closed-form Poisson-flow generative model and equilibrium matching with a quadratic flow-matching regression loss. We illustrate how this theory corrects inconsistencies in existing methods and demonstrate the effectiveness of the autonomous flow and the one-step map on ImageNet 256x256.

Lee Cheuk-Kit, Florentin Coeurdoux, Yuyuan Chen +5

1Harvard University · 2Capital Fund Management · University of Pennsylvania +2

Flow Matching One-Step Generative Modeling Flow-Based Generative Modeling Optimal Transport

Aug 2, 2026cs.LG

One-Sided Quantile Coupling for Flow Matching

Flow Matching trains continuous-time generative models by regressing the velocity field of a probability path between a simple source distribution and a target data distribution. The coupling that pairs source and target samples strongly affects optimization and sample quality, but structured couplings typically rely on mini-batch transport or assignment procedures whose cost grows at least quadratically in batch size. We propose Quantile Coupling Flow Matching (QC-FM), a lightweight one-sided coupling: rather than matching two pre-sampled batches, it samples only the data batch and constructs each paired source directly. Data ranks projected along a small number of random orthogonal directions are mapped to Gaussian quantiles, and the latent code is completed in the orthogonal complement by conditional Gaussian sampling. The construction is one-dimensional per slice, so the coupling requires no pairwise cost matrix and no assignment to solve. We show that, for each drawn frame, this coupling eliminates the irreducible regression variance along every selected slice and makes the ideal flow exactly straight there, while leaving the sampling prior unchanged: generation still starts from the standard Gaussian, and the training source deviates from it only through the copula of the slice codes, whose transport cost we bound. For training, we apply QC to an anchor subset and complete the remaining source slots with exact Gaussian samples, retaining the QC bias while preserving an explicit signal from the Baseline coupling. Across CIFAR-10, CelebA, FFHQ, and ImageNet-64, QC-FM improves over the Baseline under matched training budgets, reducing FID by up to 12.9%, and outperforms OT-CFM on all four datasets. These results suggest that preserving projected rank structure is a simple and scalable way to inject useful geometric bias into FM couplings without solving a mini-batch transport problem.

Jin-Young Kim, So-Yoon Cho, Hyun-Gyoon Kim

Independent Researcher · Division of Finance & AI, Hankuk University of Foreign Studies · Dept. of Financial Engineering, Ajou University

Flow Matching Image Generation Distribution Matching Generative Modeling Flow-Based Generative Modeling

Aug 1, 2026cs.CV

Unleashing the Power of Text: Text-Guided Flow Matching for Image Fusion under Complex Degradations

Infrared-visible image fusion under realistic degradation scenarios is a challenging task, as degradations not only cause a loss of reliable modality-specific information in observed images but also hinder the fusion process. Recent studies indicate that text can provide prior information about degradation characteristics, complementing the limited evidence available from corrupted input images and facilitating fusion. However, existing methods typically inject fixed global text representations into visual features, making it difficult for textual guidance to adapt to spatially varying degradations, local structures, and thermal saliency. To this end, we propose TGFusion, a text-guided latent-space flow matching framework that unifies degradation suppression and cross-modal fusion. TGFusion encodes task, degradation, and generation cues into structured prompts. To fully exploit these priors, we design a Prompt-conditioned Multi-stream Joint Flow Transformer that represents text as an independent semantic stream alongside fusion, visible, and infrared streams. Joint attention enables token-level bidirectional interaction and layer-wise updating among semantic and visual representations, allowing degradation semantics to dynamically guide reliable information selection and fusion latent generation. Extensive experiments on public benchmarks and complex degradation scenarios demonstrate that TGFusion achieves superior or competitive performance in perceptual quality, image naturalness, structural-detail preservation, and infrared-saliency retention, while remaining robust across diverse single and compound degradations.

Axi Niu, Jieheng Li, Kang Zhang +3

School of Computer Science, Northwestern Polytechnical University, Xi'an, China · School of Computer Science, Northwestern Polytechnical University, Xi’an, Shaanxi, China · School of Electrical Engineering, KAIST, Daejeon, Republic of Korea +2

Flow Matching Multi-Source Image Fusion Infrared-Visible Image Fusion Multimodal Fusion

Jul 31, 2026cs.RO

Safe Vision Language Action Models via Barrier Enhanced Flow Matching

This article presents a modular inference framework that integrates Flow Matching generative models with formal Control Barrier Function (CBF) safety guarantees. Unlike existing methods that apply external safety filters to a model's final output, our approach modifies the Flow Matching denoising process within the model to inherently generate safe trajectories. By employing a smooth Log-Sum-Exponential aggregate barrier, we enforce safety over entire action chunks. This aggregate barrier ensures a minimal increase in computational overhead and does not alter the semantic intent of the model. We show that, within the proposed framework, the 2-Wasserstein distance between the generated distribution and the target distribution remains bounded. Our method eliminates the need for safety-specific datasets or costly model retraining, providing a versatile solution for safe inference. We validate the approach on two robotic manipulation platforms and a 2D navigation benchmark, verifying that our framework achieves reliable safety without degrading the success rate of the model.

Kasra Sinaei, Hung-Chieh Wu, Donald Ebeigbe

The authors are with the Department of Electrical Engineering, The Pennsylvania State University

Flow Matching Control Barrier Functions Vision-Language-Action Models Safe Motion Planning

Jul 31, 2026cs.RO

Temporal Policy: History-Initialized Action Generation for Robotic Learning from Demonstration

By relying on independent couplings from uninformative Gaussian priors, standard diffusion and flow matching models are forced to learn complex, high-cost vector fields to reach the physical action space. Generative models excel at capturing multimodal behaviors for robotic Learning from Demonstration (LfD), but often suffer from high inference cost. This paper introduces Temporal Policy, a generative framework based on stochastic interpolants that formulates action generation as a temporally coupled transport problem. By initializing the generative flow at the robot's recent history, we explicitly couple past states to future action sequences. This data-dependent coupling reduces transport cost and produces straight vector fields. We validate Temporal Policy across visuomotor simulation benchmarks and on a physical Barrett WAM 2x 7DoF teleoperation platform. Our approach reduces transport costs by nearly an order of magnitude compared to noise-initialized baselines, achieving a 19.1 ms inference latency on a single NVIDIA RTX 4080. Crucially, these geometric and computational efficiencies are achieved while matching the success rates of state-of-the-art baselines. This simplified transport geometry bypasses the computational bottleneck of independent Gaussian priors, helping enable high-frequency, closed-loop control. The code is publicly available at https://github.com/dmiller12/TemporalPolicy.

Dylan Miller, Martin Jagersand

Department of Computing Science, University of Alberta, Canada

Flow Matching Robot Policy Learning Robot Skill Learning Visuomotor Policy Learning Stochastic Interpolants Robot Imitation Learning+1

Jul 31, 2026eess.AS

Stable Autoregressive Speech Generation with Low-Frame-Rate High-Dimensional Continuous Tokens

Balancing sequence length, representational capacity, and long-horizon stability is a central problem in autoregressive (AR) speech and audio generation. Representations with higher frame rates or greater capacity can preserve more signal detail, but they also make streaming generation more vulnerable to distribution drift and AR error accumulation. Conversely, shorter and more compressed representations simplify AR modeling, but their limited bandwidth may discard important components and constrain the upper bound of reconstruction fidelity and generation quality. We ask whether a low-frame-rate, high-dimensional, high-bandwidth continuous representation can be co-designed with a streaming generation framework to support robust high-fidelity reconstruction, strong single-token predictability, and superior long-horizon stability. We decompose this goal into two coupled problems: what geometric and statistical properties a high-dimensional representation space should have, and how an AR continuous-token generator should be structured to resist error accumulation. Accordingly, we propose Locodec, a locally encoded codec that shapes its representation space to improve the interpolatability of a lower-dimensional core manifold and the identifiability of the native high-dimensional coordinates, thereby improving the predictability of high-dimensional high-bandwidth tokens. We also propose MP-ELD, a single-token AR flow-matching framework that uses multi-path information routing and residual classifier-free guidance to mitigate error accumulation. Experiments with 8-Hz, 768-dimensional tokens show that our design preserves reconstruction quality, improves single-token predictability, achieves competitive WER, and maintains stable long-form synthesis, without using external SSL/ASR models, pretrained text language models, or post-training stages.

Yi Luo, Rongzhi Gu, Jixun Yao

ByteDance Seed · Work done during an internship at ByteDance Seed.

Flow Matching Audio Representation Learning Neural Audio Codecs Autoregressive Generation Audio Generation

Jul 31, 2026cs.RO

FBFM: A Training-Free Asynchronous Feedback Mechanism for Flow-Matching in World-Action Models Execution

Although world-action models (WAMs) enhance long-horizon robot control by predicting visual evolution before acting, long-horizon reliability demands repeated re-grounding in real observations--not recursive rollout. Existing WAMs address this by refreshing history or KV cache with ground-truth data between chunks. However, such chunk-wise feedback operates at a coarse temporal granularity and thus fails to correct prediction errors at the individual time-step level. To address this, we propose Feedback Flow Matching (FBFM), a training-free inference mechanism that pushes re-grounding inside the actively generated chunk. During flow matching, FBFM applies a masked pseudoinverse correction to the conditional velocity field: it leverages the preceding action chunk to guide generation of the next action chunk, and uses the image observed after executing that preceding chunk to guide the next frame prediction. This cross-chunk pairing--where feedback from one chunk arrives in time to shape the next--creates an asynchronous loop that corrects errors without waiting for chunk boundaries. Being training-free, the mechanism improves responsiveness to unexpected events and suppresses drift in long-horizon tasks. We evaluate FBFM on both a joint-generation WAM (DreamZero) and a stage-wise WAM (LingBot-VA). On selected LIBERO and RoboTwin2.0 tasks, it improves success rates by over 5% in favorable settings, and real-world robot observation-prediction diagnostics show notably better tracking. We argue that FBFM offers a new paradigm for fine-grained online correction, bridging open-loop flow generation with closed-loop real-world dynamics.

Peize Li, Ruimeng Zhang, Ru Zhang +3

DeepCybo · Zhongguancun Academy · Zhongguancun Institute of Artificial Intelligence +3

Flow Matching World Models for Robotics Action-Conditioned World Models Feedback Control World Action Models Flow-Based Generative Modeling

Jul 31, 2026eess.IV

FDIR: Harmonizing Fidelity and Human-Machine Preference in Lossy Compression Image Restoration

Image restoration quality can be evaluated along three complementary facets: pixel-level fidelity, human perception, and downstream machine preference. However, existing lossy compression restoration methods optimize for at most one of these criteria: fidelity-oriented models often regress toward conditional means and produce over-smoothed outputs, while generative approaches hallucinate plausible but factually incorrect textures that degrade both ground-truth fidelity and downstream task accuracy. To navigate this three-way tradeoff, we propose FDIR, a two-stage architecture that decouples the conflicting demands through complementary inductive biases: Quality-Guided One-Step Flow Matching (QO-Flow) recovers global semantic structure in latent space via a single forward pass, while Flow-Conditioned Detail Refinement (FCDR) deterministically restores high-frequency textures and suppresses generative hallucinations in pixel space. Extensive experiments demonstrate that FDIR achieves superior fidelity, with a favorable perceptual-fidelity balance and competitive machine preference.

Kuan-Yen Chen, Fang-Yi Su, Philip Chikontwe +1

Department of Computer Science and Information Engineering, National Cheng Kung University, Tainan, Taiwan · Department of Biomedical Informatics, Harvard Medical School, Boston, MA, USA

Flow Matching Image Restoration

Jul 30, 2026stat.ML

Conditioning Tree-Based Diffusions and Flows for Probabilistic Tabular Regression

Tree-based diffusion models fit flexible conditional predictive distributions for tabular regression without a neural density estimator, but they inherit their design defaults---noising path, parameterization, training distribution, features, sampler---from the neural setting. We show these defaults are the binding constraint: what a gradient-boosted ensemble actually solves is a supervised regression problem whose conditioning they determine. We present DiffGBM, which makes them explicit along two axes. First, a Gaussian-path flow-matching trainer for

p(y \mid x)

that learns a velocity field directly and recovers the score algebraically, admitting few-step deterministic ODE sampling. Second, we expose the score-side recipe---residualization, EDM-style preconditioning, log-sigma time sampling, noise-level features, loss weighting, and histogram resolution---as jointly tunable axes over a shared LightGBM surface rather than one frozen bundle. This \emph{score-flex} space represents the published recipe as a special case; across eleven tabular benchmarks under fold-0 tuning, folds-1--5 evaluation, and a matched 40-trial budget and sampler, the selected configurations beat that baseline on \emph{every} dataset (paired Wilcoxon

11/0

,

p<10^{-3}

), with the best aggregate CRPS skill (0.725 vs.\ 0.699) of any row. The two rows are complementary: score-flex buys accuracy with a stochastic sampler and is the slowest row, while flow matching is the cheapest sampler (

5.2\times

faster than the published baseline) and the best-calibrated DiffGBM row. Tuned non-diffusion baselines still win individual datasets, and stochastic (

\varepsilon>0

) flow samplers do not Pareto-dominate the deterministic corner.

Silas Koemen

Independent Researcher

Flow Matching Gradient-Boosted Decision Trees Tabular Diffusion Models Diffusion Sampling Score-Based Generative Modeling Diffusion Models+1

Jul 30, 2026cs.CV

WaiT for the Signal: Simple Frequency-Aware Flow-Matching

As image generation models scale to ever higher resolutions, global coherence, local detail, and texture fidelity become critical axes for generation quality. However, standard flow matching treats all spatial frequencies uniformly, ignoring the natural frequency hierarchy where high-frequency bands become indistinguishable from pure noise far earlier than coarse structures. We introduce WaiT, a Wavelet-aware image Transformer that decomposes generation into coarse and fine bands via lossless wavelets. True to its name, the high-frequency bands wait for the signal: staying pure noise until coarse structure has emerged, then joining the flow for joint refinement. Since standard FID discards fine-grained detail through aggressive downsampling, we introduce a more stringent three-axis evaluation protocol to assess quality at native resolution. On ImageNet 512x512, WaiT achieves a pixel-space FID of 1.43 and is Pareto-optimal across all three axes, reducing sampling compute by up to 50%. With our largest 2B model, we set a new state-of-the-art FID of 1.3 for pixel-space models on ImageNet 512 resolution. Our formulation outperforms even the strongest latent-space models on texture fidelity, and scales seamlessly to high-resolution OpenImages and to video generation, achieving a state-of-the-art FVD of 0.84 on Kinetics-600 with no algorithmic modifications.

Krunoslav Lehman Pavasovic, Théophane Vallaeys, Stéphane Mallat +4

1FAIR, Meta · 2École Normale Supérieure, Paris · 3Sorbonne University, Paris

Flow Matching Image Generation Video Generation Flow-Based Generative Modeling Image Generation Evaluation

Jul 30, 2026cs.CV

SCMA: Structure-Conditioned and Metal-Aware Flow Matching for CT Metal Artifact Reduction

In X-ray CT, metallic objects cause beam hardening, photon starvation, and scattering, leading to projection inconsistency, streaks, dark bands, and structural distortions that compromise clinical diagnosis and quantitative analysis. Existing metal artifact reduction (MAR) methods remain limited: optimization-based methods may leave residual artifacts or blur structures, regression networks may generalize poorly across scenarios, and generative models without sample-specific structural guidance and physical constraints may produce anatomically inconsistent structures. Flow Matching learns a continuous-time velocity field that deterministically transports a source distribution to a target distribution, providing a flexible MAR prior. However, standard unconditional Flow Matching does not exploit sample-specific structure, spatially nonuniform metal-induced degradation, or measured projections. To address these limitations, we propose SCMA, a structure-conditioned and metal-aware Flow Matching framework. First, a linear-interpolation-corrected image is fed into the velocity network with the intermediate state as a sample-specific structural condition, guiding inference toward artifact-free CT images while preserving anatomy. Second, time-varying spatial weights from the metal mask and its distance transform are incorporated into the Flow Matching loss to emphasize severe degradation within and around metal regions. Finally, conditional Flow Matching updates alternate with projection-consistency correction during inference, allowing reliable measurements outside metal traces to constrain predictions. Experiments on simulated and real CT data demonstrate that SCMA more effectively suppresses metal artifacts, preserves local anatomical structures, and reduces hallucination-like structures inconsistent with projection measurements than representative MAR methods.

Heran Wang, Jianing Sun, Xu Jiang +3

School of Mathematical Sciences, Capital Normal University, Beijing 100048, China · College of Mathematics Science, Inner Mongolia Normal University, Hohhot 010022, China · National Center for Applied Mathematics Beijing, Capital Normal University, and the Academy for Multidisciplinary Studies, Capital Normal University, Beijing 100048, China

Flow Matching Image Reconstruction Computed Tomography

Jul 30, 2026cs.LG

Enhancing Irregular Time Series Forecasting with Continuous-Time Modeling Framework

Irregular multivariate time series are widely encountered in applications such as healthcare monitoring, human activity recognition, and environmental sensing. Their core challenges stem from asynchronous observations, non-uniform sampling intervals, and the fact that temporal patterns themselves carry critical dynamic information. Existing approaches either rely on discretization-based preprocessing (e.g., interpolation, imputation, or aggregation), which disrupts the underlying continuous-time semantics, or adopt continuous-time modeling via ODE-based frameworks, which typically require specialized architectures and incur substantial computational overhead due to numerical solvers. To address these limitations, we propose WrapFlow, a continuous-time modeling framework for irregular time series forecasting. On the input side, WrapFlow introduces Continuous-Time Tokenization, which directly encodes raw observation events and explicitly models long unobserved intervals via gap-aware tokens. The resulting continuous-time tokens are then processed by a standard Transformer backbone to capture long-range temporal dependencies. On the output side, we develop a simulation-free training paradigm for Residual Flow Matching, which learns conditional residual vector fields around base predictions while avoiding numerical-solver simulation and backpropagation during training. This design enables high-quality continuous forecasting using only a small number of fixed rollout steps at inference. Extensive experiments on multiple real-world datasets demonstrate that WrapFlow achieves state-of-the-art performance.

Tianen Shen, Zhengyu Li, Yutong Li +4

Irregular Time-Series Modeling Multivariate Time Series Forecasting Flow Matching Time Series Transformers

Jul 30, 2026cs.LG

Flow Matching with Missing Data

Flow matching assumes fully observed training data, which many real-world applications rarely provide. We propose Missing-Data Flow Matching, which treats the missing coordinates of training samples as latent variables and averages the flow matching loss over the values they could take. We first prove the correction is exact rather than approximate. Under missing completely at random with true completions, the incomplete-data objective equals the complete-data objective, so missingness changes nothing about what flow matching learns and the entire difficulty relocates to the completion model. Our finite-sample analysis then answers design questions that the algorithm leaves open, and the answers are not the ones intuition suggests. Missingness transfers estimator variance rather than adding it, one completion per example already matches complete-data variance exactly, and under a fixed evaluation budget one completion is optimal. A learned completion model contributes a single irreducible bias, which we bound by its expected conditional Wasserstein distance to the true completion law. Experiments numerically validate the theoretical predictions, show that deterministic rather than frozen imputation is what collapses the generated distribution, and place our method alongside strong classical and deep imputation baselines on real tabular data.

Fairoz Nower Khan, Nabuat Zaman Nahim, Peizhong Ju

Department of Computer Science, University of Kentucky

Flow Matching Incomplete Data Imputation Learning with Missing Data

Jul 30, 2026cs.AI

The Geometry of Flow-Matching Uncertainty: A Cost-free Uncertainty Proxy and Its Application in Flow-based VLA Failure Detection

Flow matching (FM) has become a popular action head paradigm for modern embodied models. However, as a conditional generative model, it does not explicitly expose its inherent uncertainty, producing faulty action chunks even when it misinterprets the scene or encounters out-of-distribution (OOD) inputs. Therefore, determining when an FM-generated action can be trusted is essential for safe deployment, yet existing uncertainty estimation methods on real-time control suffer from several issues: extra training budget, high computational overhead, and low generalization ability. In this work, we provide a geometric interpretation of FM uncertainty in the velocity field, showing that uncertainty manifests as deviation from an ideal affine-isotropic contraction field. Building on this observation, we introduce denoising acceleration (

\mathrm{accel}

), a highly-generalizable and cost-free uncertainty proxy that measures the bending of the denoising trajectory from a single forward pass, without additional model evaluations, training, or resampling. We theoretically and empirically demonstrate that

\mathrm{accel}

is a faithful proxy for FM uncertainty and further test its utility in online failure detection. Results show that

\mathrm{accel}

identifies failing rollouts well before termination, matching or even outperforming costly resampling- and training-based baselines across settings under realistic deployment budget. Code and demos available at: https://github.com/rrrrrrzy/fm-geometry.

Ziyang Rao, Yiren Zhao, Weiyu Guo +3

1HKUST(GZ) 2HKUST 3CUHK 4AI² Roboticss

Flow Matching Uncertainty Estimation for VLA Models Flow-Based Generative Modeling

Jul 29, 2026cs.LG

SE(3)-MeanFlow: Few-Step Protein Backbone Generation on Lie Groups

Generative modeling of protein backbones promises the de novo design of proteins with prescribed structural and functional properties. Existing diffusion and flow-matching models produce high-quality backbones on SE(3)^N, but inference requires numerically integrating an ODE over hundreds of network evaluations, each involving a Lie group exponential map - a bottleneck for high-throughput design campaigns. We introduce SE(3)-MeanFlow, a few-step generative framework that extends MeanFlow from Euclidean space to the Lie group geometry of protein frames. Working natively in the Lie algebra so(3) and in R^3, we derive closed-form average-velocity identities for rotations and translations, giving simulation-free training targets. We further introduce an SE(3) alpha-Flow objective that removes the Jacobian-vector product from the rotation branch and serves as a warm-up stage, after which training switches to a small-t stabilized MeanFlow loss that is used for the remainder of pretraining and for rectification-based post-training. In protein backbone generation, SE(3)-MeanFlow matches or exceeds flow-matching baselines that use several times more sampling steps, and its advantage widens in the few-step regime, where rectification lets it lead at every matched budget - at a modest cost in diversity.

Yikun Bai, Binghang Lu, Yikai Liu +7

Department of Mathematics, Purdue University · School of Electrical and Computer Engineering, Purdue University · Department of Biochemistry, Purdue University +5

Flow Matching Lie Group Methods Generative Modeling 3D Molecular Generation Mean Flow Molecular Generation+2

Jul 28, 2026cs.CV

Noise-Robust Conditional Flow Matching: Generating Clean Samples from Noisy Datasets

Generative models learn the statistical properties of their training data, so high-quality generation depends on clean and representative datasets. In scientific imaging, acquisition often yields noisy measurements, while collecting clean references can be costly, impractical or even unattainable. Training directly on these measurements results in a model that reproduces the corrupted data. This can be circumvented by learning the clean population distribution directly from the noisy data. Conditional flow matching (CFM) combines a simple regression objective with stable training, efficient sampling, and strong image-generation performance, making it a natural framework for this setting. We introduce Noise-Robust Conditional Flow Matching (NR-CFM), an unconditional generator that learns from one corrupted observation per image. NR-CFM provides a closed-form clean endpoint correction for additive white Gaussian noise and learns a data-driven correction for general Gaussian corruptions with more complex covariance structure. Across the evaluated corruption settings, NR-CFM outperforms NR-GAN in most cases and remains competitive with Ambient Diffusion in the high-noise regime. We further evaluate NR-CFM on scientific data at signal-to-noise ratios as low as

0.001

, where it generates plausible particle images from severely corrupted measurements.

Adrian Urbański, Gabriel della Maggiora, Artur Yakimovich

Center for Advanced Systems Understanding (CASUS), Görlitz, Germany · Helmholtz-Zentrum Dresden-Rossendorf e. V. (HZDR), Dresden, Germany · Institute of Computer Science, University of Wrocław, Wrocław, Poland +2

Flow Matching Image Generation Generative Modeling Flow-Based Generative Modeling

Jul 28, 2026cs.RO

$π\mathbf{R}^2$ : Reactive Real-time Flow Policies

Generalist manipulation policies increasingly take the form of action-chunking flow policies built on large pretrained backbones. Such chunks run open-loop, so the policy cannot react to sensory input arriving mid-execution, sacrificing \emph{reactivity}. Replanning more often would restore it, but the perception-to-action pipeline (a large backbone plus multiple denoising steps) is too slow: this \emph{latency} forbids frequent replanning and leaves committed actions stale, making such policies ill-suited for dynamic, closed-loop control. We present

π\mathbf{R}^2

, which makes these policies reactive and real-time while retaining large backbones, expressive multi-modal policies, and multi-action prediction. Built on the per-position noise schedule of diffusion forcing,

π\mathbf{R}^2

contributes two ideas. First, it splits conditioning into a fast channel (proprioception, fresh every tick) and an asynchronously updated slow channel (vision-language features), so the policy reacts to proprioception within a chunk while tolerating stale vision. Second, a latency-adaptive flow schedule treats in-flight actions as inpainting conditioning and emits actions in one denoising step per call, letting one trained model adapt to varying hardware latency. Requiring minimal modification to existing architectures,

π\mathbf{R}^2

can be finetuned from a pretrained policy: applied to GR00T-N1.7 on a real xArm6+XHand platform, it replans closed-loop roughly

4\times

faster than the base policy (~

25

Hz on an A5000 GPU), acting on a fresh observation every

40

ms. Across simulation and real-world manipulation tasks,

π\mathbf{R}^2

improves the success rate by up to

23\%

in simulation and

30\%

in the real world over the strongest baseline. Project page: https://pi-r2-flow.github.io/

Sungjae Park, Shubham Tulsiani

Carnegie Mellon University

Robotic Control Flow Matching Visuomotor Policy Learning Robotic Manipulation Policy Learning

Jul 28, 2026stat.ML

Can Deep Generative Models Reproduce Non-Stationary Gaussian Random Fields?

Deep generative models (DGMs) are widely used for complex high-dimensional data and increasingly applied to spatial and spatio-temporal modeling. Their generated samples implicitly represent the learned data distribution and associated uncertainty. However, for real-world data, assessing whether DGMs have learned the underlying process is difficult because the ground truth is unknown and evaluation often relies on observations alone. We evaluate representative DGMs, flow matching (FM), DDPM, score-SDE, and VAE, on a known non-stationary Gaussian random field. This paper provides comprehensive metrics to assess recovery of the ground-truth mean and covariance structures, with oracle samples and a stationary control as references. All four models recover the mean surface, while their covariance recovery differs across model families: DDPM and score-SDE recover the covariance structure reasonably well, FM exhibits mildly attenuated non-stationarity and slight variance under-dispersion, and VAE has difficulty recovering the covariance structure. An experiment on ERA5 temperature anomalies further demonstrates how the framework can support the validation and development of DGMs for complex real-world spatio-temporal data.

Daniel Kua, Yan Song

Department of Statistics, University of British Columbia

Variational Autoencoders Flow Matching Generative Modeling Diffusion Models

Jul 27, 2026cs.LG

When Can You Correct Distribution Drift in Temporal Graph Generation? A Sharpening--Drift Tension and an Impossibility for Observation-Based Correction

Generative models of temporal graphs are trained on one stretch of an evolving network and deployed on the next, and they degrade badly in the gap. We show this degradation is derivable, general, and not fixable from observations. The masked flow-matching loss decomposes exactly, with no independence assumption, into an irreducible entropy plus a divergence whose derivative along the training path is positive precisely for structures rare during training and common at deployment, diverging as their training probability goes to zero. Empirically the trade-off is a power law with exponent

-0.605

(

R^2=0.9977

), and drift raises the sampler's error floor without changing how many steps reach it: across seven well-powered conditions the drift-period marginal error varies by at most

6\%

over a

50\times

range of sampling budgets, while the floor sits

2.2\times

to

34.3\times

above the in-period floor. Because the deployment period is observed, correction looks like a matter of measurement. It is not. We prove that any corrector measurable with respect to past observations leaves at least the conditional variance of the statistic it tracks, and that trend extrapolation beats trusting the last observation only when

μ^2>v(1-2ρ)

. Both premises are measurable and both go the wrong way: the drift is trendless and mean-reverting, with a one-step innovation as large as the drift itself. An oracle removes

60\%

of the error, the best observation-based corrector recovers

5.7\%

of that, and extrapolation is strictly worse than doing nothing clever.

Tianpeng Li, Xuan Guo, Wenjun Wang +2

College of New Media and Communication, Tianjin University · School of Artificial Intelligence, Tianjin University · School of Cyberspace Security,Hangzhou Dianzi University

Flow Matching Distribution Shift Graph Generation Generative Modeling Flow-Based Generative Modeling Drifting Models+1

Jul 27, 2026cs.LG

Joint Flow Matching for Generator-Consistent Classification

We introduce Joint Flow Matching (JFM), a training framework for continuous normalising flows over multiple variables. Standard flow matching transports variables from noise to data simultaneously, offering no natural mechanism for forward and reverse conditional inference from a shared joint model. JFM resolves this by assigning opposite roles to each variable at the temporal endpoints. We prove that JFM produces a consistent joint distribution where that forward or reverse integration are conditionals of the same joint. We explore this consistency in the context of joint classification and generation as the basis for interpretability in discriminative-generative models. We validate JFM on conditional datasets producing competitive accuracy with inherently well-calibrated confidence scores without post-hoc calibration, and classifier-consistent image generation.

Hayden McAlister, Lech Szymanski

School of Computing University of Otago Dunedin, New Zealand

Flow Matching Continuous Normalizing Flows Flow-Based Generative Modeling Conditional Generative Modeling

Jul 26, 2026cs.IR

Escaping the Euclidean Void: Manifold-Informed Flow Matching for Sequential Recommendation

Conventional recommenders capture users' preferences by optimizing observed user-item relations, whereas continuous generative recommendation additionally learns the trajectory of synthesizing a target item. Flow matching drives this process by gradually shaping initial noise into a definitive next-item representation through intermediate states in a continuous embedding space. However, item catalogs are discrete and sparsely supported, meaning even a straight Euclidean path can cross continuous regions that contain little evidence of valid item semantics. Formalizing this failure as the Euclidean void, we propose MIRAGE, a Manifold-Informed Rectification framework for Accelerated Generation of Embeddings in sequential recommendation, which rectifies the learned embedding geometry around an unchanged straight probability path. By leveraging an item co-occurrence graph as a proxy for the underlying semantic manifold, MIRAGE aligns interpolated path states with local anchors, reorganizing the embedding space to ground the trajectory in valid item support. MIRAGE retains the original probability path and uses the graph only during training, thereby enabling accurate and efficient one-step inference. Extensive experiments on four real-world datasets reveal that MIRAGE consistently outperforms state-of-the-art baselines, effectively boosting performance on sparsely observed targets while achieving robust overall accuracy. Our code will be made publicly available upon publication.

Dengzhao Fang, Jingtong Gao, Yu Li +2

Jilin University · City University of Hong Kong

Flow Matching Sequential Recommendation One-Step Generative Modeling Manifold Learning Generative Recommendation

Jul 26, 2026cs.LG

Restoration Flow Matching-Based Channel Refinement and Equalization Correction for MIMO Semantic Communications

In multiple-input multiple-output (MIMO) semantic communication, imperfect channel state information (CSI) and equalization mismatch can seriously degrade semantic reconstruction quality. To address this issue, we propose a unified restoration flow matching (RFM)-based framework for channel refinement and equalization correction. Specifically, the channel RFM (CRFM) module is developed to refine the coarse channel, thereby improving channel estimation accuracy. Based on the refined channel, the developed semantic RFM (SRFM) module is employed to correct the residual distortions in the post-equalization latent space. The key idea is to formulate the two cascaded inverse problems of channel estimation and equalization as the unified conditional restoration task, in which the learned conditional velocity field guides the perturbed distribution towards the target distribution. To enhance the robustness of these two modules under various distortion conditions, we develop a dual-anchor perturbation training strategy that jointly learns near-manifold refinement and large-error correction, and implement inference through a few-step deterministic ordinary differential equation (ODE) solver. Extensive experiments on MIMO channels and visual semantic transmission tasks demonstrate that the proposed scheme improves key metrics for channel estimation and semantic reconstruction quality. Moreover, compared with representative diffusion-based generative baselines, the proposed method requires fewer sampling steps.

Wenkai Liu, Nan Ma, Jianqiao Chen +3

State Key Laboratory of Networking and Switching Technology, Beijing University of Posts and Telecommunications, Beijing 100876, China · ZGC Institute of Ubiquitous-X Innovation and Applications, Beijing 100876, China · Cooperative Medianet Innovation Center (CMIC) and the Department of Electronic Engineering, Shanghai Jiao Tong University, Shanghai 200240, China

Flow Matching Semantic Communication Channel Estimation

Jul 25, 2026stat.ML

Logit-Coordinate Generative Models for Mixed Continuous-Categorical Tabular Data

Mixed continuous--categorical data pose a representation problem for continuous generative models. Flow Matching and Gaussian diffusion operate in Euclidean spaces, whereas categorical laws lie on probability simplices and may be highly imbalanced. We study a logit-coordinate framework that encodes categorical variables as smoothed natural parameters and combines them with transformed numerical variables. This yields common formulations of Logit Flow Matching and Logit Diffusion. We introduce a mixed-distribution discrepancy separating categorical marginal error from conditional continuous Wasserstein error, and derive stability bounds and imbalance-aware nonparametric rates linking vector-field or drift error to decoded mixed-distribution error. Controlled simulations show that scaled-logit coordinates improve or match one-hot coordinates, especially under severe rare-cell imbalance. Across four real-data benchmarks and ten splits per dataset, Logit FM improves the primary distributional metrics on three datasets and is comparable on Churn2; Block-Conditional Logit FM consistently improves the flat model; and Logit Diffusion generally improves over or matches One-Hot Diffusion.

Yuefei Shen, Xiaotong Shen

School of Statistics, University of Minnesota

Flow Matching Synthetic Tabular Data Generation Generative Modeling Diffusion Models

Jul 24, 2026cs.LG

FMOPF: Latent Flow Matching with Constraint-Aware Interaction Priors for AC Optimal Power Flow

AC optimal power flow determines the minimum-cost generation dispatch under nonlinear power balance constraints and is solved thousands of times daily in electricity market operations. Learning a direct mapping from load conditions to OPF solutions can accelerate this computation, yet with deepening renewable penetration, a single optimal dispatch is no longer sufficient. Operators require a characterization of the distribution of feasible near-optimal solutions for risk quantification, sensitivity analysis, and multi-objective trade-off assessment. Supervised neural networks provide fast point predictions but cannot capture this conditional distribution. Diffusion-based generative models can sample diverse solutions in principle, yet existing methods operating in the raw state space exhibit degraded solution quality and fail to scale beyond medium-sized systems. We identify the root cause as the conflation of two distinct tasks within a single model. Compressing the high-dimensional OPF solution manifold is one task, and learning the conditional mapping from loads to that manifold is another. This paper presents FMOPF, a framework that resolves this conflation by decoupling compression from generation through latent flow matching and by explicitly modeling load-state coupling through a Constraint-Aware Interaction Prior Network. Experiments on four IEEE test systems demonstrate that FMOPF provides the most effective Newton-Raphson warm starts, achieves the lowest tail risk among generative methods, and is the first such method to scale to systems with several hundred buses while preserving full feasibility. Ablation studies confirm that the latent generation pipeline is a necessary condition for physical feasibility and that the interaction prior functions as a late-stage tail-risk controller.

Zhilin Huang

China Southern Power Dispatching and Control Center, China Southern Power Grid

Constrained Generative Modeling Flow Matching Uncertainty Quantification Optimal Power Flow Constrained Optimization Power Systems