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

Sep 22, 2026cs.LG

OMatG-flash: An All-Atom Flow Map with Reinforce Adjoint Matching for Scalable Materials Discovery

The discovery of novel inorganic materials drives technological breakthroughs in critical fields such as computing and energy storage. Generative AI has promised to accelerate the materials discovery pipeline, but state-of-the-art flow and diffusion models remain bottlenecked by the cost of proposing candidate materials. To address this, we introduce OMatG-flash, an all-atom flow map for inorganic crystal structure prediction (CSP) and de novo generation (DNG). OMatG-flash is a Pareto-optimal inference engine for materials, sampling candidate materials with an order of magnitude fewer inference steps and less wall-clock time than existing flow and diffusion models while demonstrating benchmark performance on par with the state-of-the-art. To enable post-training fine-tuning we apply Reinforce Adjoint Matching to flow maps, further improving match rates and RMSE on the unconditional CSP task. OMatG-flash showcases the potential of flow maps to accelerate generation of high-quality candidate inorganic materials and demonstrates a step forward in sample throughput necessary for data-hungry materials discovery workflows.

Thomas Egg, Harry Winston Sullivan, Ellad B. Tadmor +1

New York University · University of Minnesota

Flow Matching Crystal Structure Prediction Inference Acceleration Crystal Structure Generation

Sep 22, 2026cs.LG

Gaussian Flow-Matching Schedules: Implications for Sampling and Training

Flow-matching schedules affect both sampling dynamics and the variance of the regression target. For centered commuting Gaussians, we show that a direction-dependent schedule decomposes into two independent design choices: a variance path, which fully determines the intermediate laws and probability flow, and a factorization, which leaves this flow unchanged while controlling irreducible regression variance. On the sampling side, we analyze finite-step Euler accuracy and derive a necessary drift bound for exact N -step sampling, connecting the geodesic and the logarithmic path. On the training side, for any fixed path, we derive closed-form factorizations that either minimize time-averaged regression variance or make it constant along the path.

Arsène Claustre, Hugo Negrel, Claire Boyer +2

DI-ENS · CNRS, ENS Paris · DMA, CFM +6

Flow Matching Diffusion Sampling Flow-Based Generative Modeling Variance Reduction

Sep 22, 2026cs.RO

History-Conditioned Flow Matching for Probabilistic Dynamics of Tendon-Driven Continuum Robots

Deterministic dynamics modeling of tendon-driven continuum robots remains challenging owing to uncertainties in material behavior, tendon transmission, friction, and contact. Measured joint configurations and nominal tendon commands do not fully characterize these internal mechanical factors, leaving uncertainty in the subsequent motion. We therefore develop a history-conditioned, physics-informed flow-matching framework for probabilistic dynamics prediction, using motion and actuation histories to predict the distribution of the next complete joint configuration. By recursively sampling next-step configurations under prescribed commands, the model predicts distributions of future whole-body motions. In simulation, scenario-specific models achieve five-second trajectory Energy Scores (lower is better) of 12.05 mm under internal friction variation and 9.29 mm under unobserved actuation disturbances. Relative to the conditional variational autoencoder and diffusion baselines, Flow attains lower Energy Scores and coverage closer to the nominal level in both scenarios. Ablations support history and structural conditioning in both scenarios. On the physical robot, predictions under two tendon-command profiles excluded from training capture the principal motion sequences, with five-second Energy Scores of 11.91 and 11.42 mm, lower than the compared baselines. The predicted-to-measured spread ratios are 1.65 and 1.22 (closer to 1 is better). These results support history-conditioned probabilistic dynamics prediction under incomplete mechanical observations.

Hang Yang, Tingcong Liu, Junjie Xiong +2

Flow Matching Robot Dynamics Learning Tendon-Driven Actuation Soft Robotics

Sep 21, 2026cs.CV

Classifier-Free Guidance in Flow Matching: Non-Autonomous Potentials, Overshoot, and Posterior-Mean Control

Classifier-free guidance (CFG) improves conditional generation in Flow Matching, but strong guidance can distort the generated distribution and reduce diversity. We provide a geometric account of this behavior by viewing Flow Matching as a time-varying gradient flow and characterizing how CFG reshapes its underlying potential. This view explains how stronger alignment can be accompanied by mean displacement and trajectory concentration, and motivates controlling guidance through the model-implied terminal posterior mean. We therefore propose Posterior-Mean-Capped CFG (PMC-CFG), a training-free, per-sample method that adaptively retains the strongest feasible guidance without additional network evaluations. Experiments on synthetic and large-scale image-generation benchmarks show that PMC-CFG limits guidance-induced distortion and concentration while improving the alignment--diversity trade-off, with particularly strong benefits when nominal guidance is large.

Jishen Peng, Zheng Ma

School of Mathematical Sciences, Shanghai Jiao Tong University, Shanghai, China · Institute of Natural Sciences, MOE-LSC, Shanghai Jiao Tong University, Shanghai, China · Qing Yuan Research Institute, Shanghai Jiao Tong University, Shanghai, China +1

Flow Matching Classifier-Free Guidance Conditional Image Generation Flow-Based Generative Modeling

Sep 21, 2026cs.RO

Object-Centric Conditioning for Visuomotor Flow Matching

Robot visuomotor policies are commonly formulated as autoregressive, diffusion-based, or more recently, flow matching models. Among them, Action-to-Action (A2A) flow matching improves inference efficiency by initializing generation from historical action priors rather than stochastic noise. However, stale historical motion patterns and entangled global visual representations can jointly reduce robustness under spatial out-of-distribution (OOD) shifts and visual distractors. In this work, we propose SlotFlow, an object-centric flow matching policy for robust visuomotor manipulation. SlotFlow decouples scene observations into semantic ("what") features and lightweight image-plane spatial ("where") cues to provide object-aware policy conditioning and current-state grounding. The semantic representation suppresses irrelevant background correlations, while the spatial cue improves adaptation to shifted object configurations. Extensive simulation and real-world experiments demonstrate improved robustness under visual distractors and severe spatial perturbations while preserving the low-step inference efficiency of A2A. Controlled initialization and perception ablations further identify object-centric grounding as a major source of the gains and show that it complements, rather than replaces, useful historical motion priors.

Jijie Li, Xu Yang, Junhong Zou +4

School of Artificial Intelligence, University of Chinese Academy of Sciences · State Key Laboratory of Multimodal Artificial Intelligence Systems, Institute of Automation, Chinese Academy of Sciences · Foundation Model Research Center, Institute of Automation, Chinese Academy of Sciences +2

Flow Matching Visuomotor Policy Learning Robotic Manipulation

Sep 21, 2026eess.AS

P2Flow: Phoneme-aware Progressive Flow Matching for Extreme Speech Super-Resolution

Generative models have recently demonstrated considerable promise in speech super-resolution (SSR). Nevertheless, the majority of existing work has concentrated on standard or versatile SSR configurations, leaving the extreme setting with severely limited spectral inputs largely unexplored. In this regime, current approaches exhibit marked performance degradation, underscoring the need for dedicated solutions. To bridge this gap, we introduce P2Flow, a phoneme-aware progressive flow matching (FM) framework designed for extreme SSR with three main strategies. First, our model leverages phonetic information to reconstruct missing spectral components. Furthermore, it employs a progressive architectural design that hierarchically restores distinct frequency regions. Finally, we incorporate post-training of the vocoder to enhance overall waveform fidelity. Extensive experiments are conducted on the TIMIT and VCTK datasets under both 1 kHz to 16 kHz and 2 kHz to 16 kHz settings, demonstrating that P2Flow yields state-of-the-art results across multiple evaluation metrics.

Ningyuan Yang, Yize Li, Pu Zhao +5

Stony Brook University, NY, US · Northeastern University, MA, US · UIUC, IL, US +1

Flow Matching Speech Processing Speech Enhancement

Sep 20, 2026cs.RO

FeasibleFlow: One-Step Joint Transport of Configuration Feasibility and Trajectories for End-to-End Driving

End-to-end autonomous driving maps current observations directly to future trajectories, yet those trajectories must remain valid as the scene evolves. Future state modeling aims to address this temporal mismatch, but general representations often contain information unrelated to ego planning and affect trajectory generation only through auxiliary supervision, static conditioning, or proposal evaluation. We propose FeasibleFlow, a one-step end-to-end generative framework that jointly transports a configuration-space feasibility field and multimodal ego trajectories. Our Asymmetric Joint MeanFlow uses the pathwise Jacobian-vector product in the MeanFlow identity to incorporate field evolution into trajectory transport. Because safety feedback is sparser than progress feedback, we further introduce the Anchor-relative ranker (ARR) and Pareto-ReinFlow to balance safety and progress in candidate selection and generation, respectively. Experiments on the NAVSIM benchmark demonstrate the strong performance of FeasibleFlow and validate both the joint transport of feasibility and trajectories and the proposed safety-first mechanisms.

Xiang Li, Bikun Wang, Qing Xu +1

Cross-Domain Computing Solutions, Bosch

Flow Matching Trajectory Generation End-to-End Autonomous Driving Safe Motion Planning Autonomous Driving Planning

Sep 20, 2026stat.ML

Bayesian Filtering in Physical Systems via Test-time Trained Flow Matching

Bayesian filtering provides a principled framework for online state estimation under uncertainty, yet its application to systems with high-dimensional states and complicated posterior distributions remains challenging. Recent generative models, such as flow matching, have shown potential in Bayesian filtering. However, they still rely on particle-based representations of the posterior, which lose the rich information of the full distribution, or tackle a trajectory-level inverse problem that conflicts with the recursive structure of Bayesian filtering. To address this, we propose a new perspective of directly encoding the evolving distribution into flow matching model weights, namely, the Belief Flow Filter (BFF). It is a generative filtering framework that updates model weights via gradient descent at test time to track the posterior evolution. Thereby, BFF bypasses the scalability issue of particle representations or the flexibility limitation of Gaussian assumptions in conventional filters. We theoretically justify that the BFF design is structurally aligned with Bayesian filtering, and its training objective targets the recursive filtering operator. BFF is empirically verified across 5 different physical systems, including ones with chaotic dynamics and highly sparse, non-linear observations. The results show that BFF attains the best score in 8 of 9 metric-benchmark cells across the three standard 1D and 2D PDE benchmarks, and similarly leads on the extreme single-moving-sensor setting and on a real-world-grounded tokamak plasma estimation task, demonstrating its potential to accurately approximate the Bayesian filtering operator in high-dimensional probability space.

Ruiqi Feng, Chongyi Wang, Tao Zhang +1

Westlake University & Zhejiang University · Westlake University

Flow Matching Bayesian Filtering Conditional Distribution Estimation

Sep 18, 2026cs.LG

$λ$ -Controlled GRPO: Turning Flow-Matching Ratio Instability into a Budgeted Resource

Reinforcement learning is increasingly used to align image generators with reward signals, and Flow-GRPO recently extended this paradigm to flow-matching models by treating the denoising sampler as a stochastic policy that can be optimized from reward feedback. Training in this setting is unstable in a way specific to multi-step denoising: the policy update changes systematically across denoising steps, with importance ratios drifting below one, becoming increasingly dispersed, clipping at different rates, and leaving fewer usable samples late in training. Prior work treats these effects as separate failure modes and addresses each with a hand-tuned stabilizer. We show instead that they arise from a single per-step quantity, which we call path variance. This quantity is determined exactly by the sampler's Gaussian transition kernel and can be estimated cheaply during training. This reframes instability as a resource that can be measured and budgeted rather than a collection of symptoms to repair. Our method,

λ

-Controlled GRPO, calibrates importance-ratio behavior from this predicted law rather than from noisy empirical statistics, and allocates gradient effort across denoising steps according to their predicted cost. The two scales governing the update are fixed by standard policy choices rather than introduced as free tuning parameters. On a text-to-image model under two reward settings, rendering difficult target text scored by optical character recognition and matching human preferences scored by a preference model,

λ

-Controlled GRPO improves both text accuracy and preference reward over the strongest empirical stabilizer. It also keeps late-step path variance within its intended budget, precisely where the baseline systematically overshoots. The result is a Flow-GRPO update calibrated by its own transition law rather than stabilized after instability appears.

Yufeng Wang, Parivesh Priye, Meeshawn Marathe +1

Stony Brook University · Georgia Institute of Technology · Rivian and Volkswagen Group Technologies

Flow Matching T2I Generation Group Relative Policy Optimization RL for Image Generation Flow-Based Generative Modeling

Sep 17, 2026cs.CV

FlowSGS: Improving Flow Matching Priors for Inverse Imaging with Stochastic Interpolants

Flow matching has emerged as the state-of-the-art generative model and has been used for plug-and-play (PnP) priors to solve inverse problems in computational imaging. However, existing flow-based inverse solvers assume linear forward models and/or make simplifying approximations in posterior sampling. To circumvent these problems, we introduce FlowSGS, a flow-based posterior sampling method using Split Gibbs Sampling (SGS) to decompose the posterior into a likelihood step and a prior step. Specifically, we sample from the likelihood step using Langevin dynamics and leverage the Stochastic Interpolants (SI) framework to integrate a pretrained flow model into the prior step. We provide a form for the prior step that uses SI's reverse-time SDE, and show connections to previous PnP methods. Moreover, with the aid of the flow prior's straight probability paths and a novel timestep correction technique for the reverse-time SDE, FlowSGS requires fewer network evaluations in its prior step than plug-and-play diffusion samplers. Our experiments show state-of-the-art performance on a range of inverse problems. For the first time, we provide an experiment on a nonlinear inverse problem (Fourier phase retrieval) for flow-based inverse solvers.

Tianao Li, Xinhui Qian, Emma Alexander

Department of Computer Science, Northwestern University · NSF-Simons AI Institute for the Sky (SkAI) · Department of Statistics and Data Science, Northwestern University

Flow Matching Markov Chain Monte Carlo Posterior Sampling Flow-Based Generative Modeling Image Inverse Problems

Sep 17, 2026cs.RO

TraceFlow: Guiding Frozen Flow-Matching Robot Policies with Success and Failure Traces

A vision-language-action (VLA) policy with a flow-matching action expert generates each action chunk (a short command sequence) by integrating a learned velocity field; once its weights are fixed, the success or failure of an earlier rollout cannot change the chunk generated now. Concurrent test-time methods give a frozen policy such an input from retrieved successes, a learned critic, a verifier, or a dynamics model, but none uses the robot's own failed rollouts as negative evidence with nothing but a terminal outcome bit. We introduce TraceFlow, a progress-aligned guidance field that turns the action densities of retrieved successful and failed rollouts into a bounded correction to a frozen flow-matching action expert, using one terminal outcome bit per rollout and no other label. Its TraceBank stores traces, time-ordered state-action records with a terminal label, starts from the target-task training traces, and later admits the deployed robot's own rollouts. On an ordered real-robot packing task the base completes 21 of 50 trials in order, TraceFlow 39, and one stacking round without any weight update 47, with wrong-sequence episodes falling from 20 to 0. In simulation the gain is selective: with per-suite selected settings, TraceFlow raises RoboMemArena Sequence from 78.92% to 91.50% task success and Transferring from 54.41% to 62.00% at stacking round 2, leaves the 26-task aggregate unchanged, lowers Counting and Occlusion by 1.12 and 1.42 points, and changes LIBERO-Plus (Long) by +1.27 points (p = 0.0733). Stacking gains are finite, every branch peaking before round ten, and the bank's success-to-failure ratio predicts no retrieval allocation. Project page: https://zhangjiaxuan-xuan.github.io/TraceFlow/

Jiaxuan Zhang, Ruizhe Liu, Yu Zhang +1

The University of Hong Kong, Hong Kong SAR, China. · Southern University of Science and Technology, Shenzhen, China. · HKU InfoBodied AI Lab

Flow Matching Robot Policy Learning Test-Time Adaptation of VLA Models

Sep 17, 2026cs.LG

Dynamic Generalized Gromov-Wasserstein Optimal Transport

Gromov--Wasserstein optimal transport (GW-OT) extends classical optimal transport by introducing structure-aware transport cost. This is particularly relevant for spatial transcriptomics, where dynamical reconstruction should preserve tissue structure in addition to matching expression patterns. While static formulations have been widely used for such structure-aware alignment, a general dynamic formulation for reconstructing continuous trajectories is still missing. We introduce Travelling Pair Dynamical Alignment and Trajectory Estimation (TP-DATE), a theoretical and computational framework to generalize GW-OT dynamically in a simulation-free manner. We formulate a broad class of static and dynamic Quadratic-form OT (QOT) through path actions and prove the static dynamic equivalence. We further develop travelling-pair flow matching, which allows interacting conditional paths and marginalizes their interactions into a single vector field. On synthetic and real spatial transcriptomics data, TP-DATE better preserves spatial structure and improves continuous 3D dynamics reconstruction.

Junda Ying, Zhiwei Zeng, Peijie Zhou +1

Beijing International Center for Mathematical Research, Peking University · Center for Quantitative Biology, Peking University · Center for Machine Learning Research, Peking University +4

Flow Matching Trajectory Inference Optimal Transport

Sep 16, 2026cs.LG

How to Guide Your Language Flow

We introduce a new method to guide flow matching models. Our approach, which we call probe guidance, uses the frozen internal states of an existing diffusion model to construct a guidance signal. This works using a similar principle as autoguidance, but eliminates the need for an additional forward pass at inference time and provides a reliable path to ensure that the weak and strong model share similar dynamics. We apply and benchmark this method on continuous diffusion language models, where probe guidance sets a new state-of-the-art performance on unconditional generation. When applied to a 1.7B diffusion language model, probe guidance consistently improves on multiple choice question answering benchmarks. Using our probes, we study the traditional autoguidance setting where the strong model is a weak checkpoint, and find that the weak model must come from a low-entropy region of training. These findings both provide a practical way to improve diffusion language models and shed light on the actual mechanism behind autoguidance, which is currently poorly understood.

Rohit Dilip, Tianrong Chen, Yuyang Wang +3

Apple · Caltech

Flow Matching Diffusion Model Guidance Diffusion Guidance Diffusion Language Model Inference Flow-Based Generative Modeling Diffusion Language Models+1

Sep 16, 2026cs.CV

Beyond Random Couplings: Contrastive Noise Alignment in Generative Flows

Diffusion and flow-matching models are typically trained by corrupting data through independently sampled Gaussian noise. While simple and scalable, this forward process induces arbitrary data-noise couplings, forcing the network to learn high-curvature transports between unrelated endpoints. Existing optimal-transport methods reduce this burden by reassigning fixed noise samples to data, but the source noise distribution itself remains passive. To address this, we introduce Contrastive Noise Alignment (CNA), a training-time method that creates dynamic, contrastive couplings by optimizing the noise representations directly. By modeling the noise batch as an interacting particle system, CNA employs a cross-modal InfoNCE objective to align noise particles with their paired data targets. To prevent spatial collapse, this alignment is regularized using an angular entropy term and a radial norm penalty. We show theoretically that this equilibrium asymptotically preserves Gaussian structures, maintaining tractability during inference. Empirically, CNA improves the alignment between noise and data, reduces flow curvature, and provides better generation quality with fewer required sampling steps. For few-step, pixel-space generation (2-4 NFEs), CNA reduces FID by over 50% compared to standard rectified flow, and by at least 24% against Optimal Transport baselines.

Lennart Wittke, Vinicius Azevedo

ETH Zürich · Disney Research | Studios

Flow Matching Cross-Modal Alignment Pixel-Space Diffusion Models Few-Step Diffusion Sampling Flow-Based Generative Modeling

Sep 15, 2026cs.LG

Same Flow, Different Paths: Variance Reduction in Flow Matching

In flow matching (FM), a velocity model

v_θ

is trained using a predefined path

g_t

that connects data and noise samples (e.g.,

g_t(x_0, x_1) = (1 - t) x_0 + t x_1

). In this work, we study the choice of this path from an optimization perspective by analyzing the variance of stochastic gradients. We consider the class

G(p_t,v^\star_t)

of paths that induce the same marginal distributions

p_t

and marginal velocity field

v^\star_t

, and therefore the same FM objective. Our main finding is that the choice of path

g_t

can fundamentally change the convergence rate of SGD, even when the FM objective remains exactly the same. (i) For a linear velocity model and one-dimensional Gaussian data, we derive a tight bound on the SGD iteration complexity up to logarithmic factors and find an analytically optimal path that minimizes this bound among linear paths inducing the same FM problem. (ii) We then extend the variance analysis to general FM problems and formulate path selection at a fixed

θ

as the variance-minimization problem PathOpt

_θ

, constrained to

g_t\in G(p_t,v^\star_t)

. We show that this constraint is essential: reducing variance without it can lead to slower convergence. (iii) Since the constraint

g_t \in G(p_t,v^\star_t)

cannot generally be verified directly, we derive an equivalent formulation with constraints that can be estimated from samples, allowing paths to be found numerically. Our theoretical results are supported by experiments with Gaussian data, Gaussian mixture models, and real datasets.

Alexander Tyurin

AXXX, Moscow, Russia · Applied AI Institute, Moscow, Russia

Flow Matching Stochastic Optimization Convergence Flow-Based Generative Modeling Variance Reduction Stochastic Gradient Descent

Sep 15, 2026cs.LG

MyoFlow: Anchor-Tied Rectified Flow for HD-sEMG Gesture Recognition Across Sessions and Subjects

High-density surface electromyography (HD-sEMG) gesture recognition supports prosthetic control, assistive robotics, and rehabilitation, but electrode re-donning and physiological variability cause distribution shifts that degrade accuracy across sessions and subjects. Generative HD-sEMG models primarily synthesize signals for augmentation; although diffusion models enhance representation learning, prediction still relies on a separate classifier. To tie learned dynamics to the decision rule, we propose MyoFlow, the first discriminative flow-matching framework for HD-sEMG recognition across sessions and subjects. It recasts classification as anchor-tied transport: a domain-conditioned rectified flow moves encoded windows toward gesture anchors that serve as transport targets and define the nearest-anchor decision geometry, enabling zero-shot recognition without an independent head. On the Hyser dataset, MyoFlow improves mean cross-session and cross-subject accuracy over the strongest diffusion-based baseline by 4.24% and 6.37%, respectively, and achieves 91.71% mean zero-shot accuracy and 97.39% mean few-shot accuracy across multiple days on the CEMHSEY dataset.

Chenhao Wu, Dingjie Peng, Zhihe Zhang +6

Waseda University, Japan · KDDI Research Inc., Japan · The University of Manchester, UK

EMG-Based Gesture Recognition Flow Matching Rectified Flow Domain Generalization

Sep 15, 2026cs.CV

MedPCFM-TED: One-Step Point Cloud Flow Matching for Implant Generation via Teacher-Guided Endpoint Distillation

Cranial implant generation is an important task in medical imaging. Recent point cloud based generative methods, particularly flow matching, offer strong reconstruction quality and efficient sampling, but still require multiple neural function evaluations during inference. This limits rapid generation of multiple plausible implant candidates. We propose Teacher-guided Endpoint Distillation (TED), a simple one-step distillation framework for conditional cranial implant generation on point clouds. TED trains a one-step student using teacher-guided endpoint supervision and geometric matching losses, while avoiding explicit path straightening. We evaluate TED on the SkullFix and SkullBreak benchmarks. TED achieves the best overall performance on the SkullBreak dataset, remains competitive on SkullFix, and provides the strongest Chamfer distance performance among the compared one-step methods. In addition, TED generates implants in approximately 0.04s per sample. These results show that one-step distillation can substantially accelerate conditional point cloud implant generation without sacrificing reconstruction quality.

Kamil Kwarciak, Marek Wodzinski

Department of Measurement and Electronics, AGH University of Krakow, Krakow, Poland · Sano Centre for Computational Medicine, Krakow, Poland

Flow Matching One-Step Generative Modeling Point Cloud Generation Medical Image Synthesis Knowledge Distillation

Sep 15, 2026cs.LG

FlowATC: Aircraft Trajectory Prediction via Flow Matching

Building accurate decision-support tools for next-generation air traffic control requires robust trajectory prediction models. We present a flow-matching architecture trained exclusively on historical aircraft trajectories, with no route labels or chart supervision. Trained on 1.15 million Automatic Dependent Surveillance-Broadcast trajectory windows collected over the San Francisco Bay Area, the model generates aircraft trajectory distributions that closely match historical traffic, reproducing known airspace structure around San Francisco Airport such as the shape of SFO's published NIITE FOUR departure procedure. Our model is trained directly on the native, irregular ADS-B sampling interval. Trajectory prediction is cast as sequence inpainting using a block-causal Transformer that denoises future state tokens conditioned on the observed history using Conditional Flow Matching or Denoising Diffusion Probabilistic Models. We compare our architecture against constant-velocity, deterministic-Long Short Term Memory, and Conditional Variational Autoencoders baselines. At matched parameter count, CFM outperforms DDPM by 11-26% in minADE@20, and both generative objectives surpass the CVAE baseline by 31-41%. We further show that the error degrades gracefully with prediction horizon, and the architecture remains effective when retrained on temporally decimated feeds. Lastly, we sample

K

independent completions, yielding spatial probabilistic occupancy estimates that can serve as input to downstream conflict-risk estimation.

Mathurin Petit, Emir Torun, Louis Brusset +2

École Polytechnique, Palaiseau, 91128, France · Technische Universität Berlin, Berlin, 10623, Germany · Mines Paris–PSL University, Paris, 75006, France +2

Flow Matching Air Traffic Management Flow-Based Generative Modeling Trajectory Prediction Diffusion Models

Sep 14, 2026cs.LG

Generative models for simulation based filtering: Formulations and Empirical Comparisons

This letter presents a unified formulation and a controlled numerical comparison of generative-model approaches to the nonlinear filtering problem. Under this formulation the analysis step is realized by a transport of the forecast distribution to the posterior, the approaches differing only in how that transport is selected and learned. We derive three new filters, based on stochastic interpolants, their deterministic flow-matching limit, and Schrödinger bridges realized through forward--backward SDEs. We develop a two-stage tuning procedure that separates the training of the generative model from its online refinement. The resulting methods are compared against the optimal transport filter (OTF), the Knothe--Rosenblatt filter (KRF), the sequential importance resampling (SIR) particle filter and the ensemble Kalman filter (EnKF), in terms of accuracy, computational time, and sensitivity to ensemble size and state dimension. The results indicate that every generative filter resolves multimodal posteriors that the EnKF and SIR do not, that no single generative framework dominates, the preferred method being set by the available online budget and ensemble size, and that the filters differ in the regularity of the particle trajectories they produce.

Mohammad Al-Jarrah, Wei Deng, Bamdad Hosseini +1

Department of Aeronautics & Astronautics, University of Washington, Seattle · Department of Applied Mathematics, University of Washington, Seattle · ML Research, Morgan Stanley

Flow Matching Schrödinger Bridges Stochastic Interpolants

Sep 14, 2026cs.LG

Principal-timestep Restricted Init via Sparse Matrix-decomposition in Flow-matching

Flow-matching diffusion models have recently emerged as a strong paradigm for high-fidelity visual generation. However, their prohibitively high fine-tuning cost limits scalability to downstream tasks. While Low-Rank Adaptation (LoRA) combined with spectral initialization has demonstrated accelerated convergence and improved performance in autoregressive language models by better aligning gradient directions, we find that it fails to deliver similar gains in diffusion fine-tuning, often yielding marginal or even negative improvements over vanilla LoRA.We attribute this discrepancy to a fundamental mismatch between LoRA's low-rank parameterization and the intrinsically high-rank gradients induced by the flow-matching objective. In particular, stochastic timestep sampling introduces directionally heterogeneous gradient signals across training steps, leading to misaligned updates under low-rank constraints.To address this issue, we propose Prism-LoRA,a Principal-timestep Restricted Init via Sparse Matrix-decomposition framework that improves gradient alignment during fine-tuning. Our method consists of two key components: (i) principal timestep selection, which restricts initialization gradients to a subset of dominant timesteps to suppress effective gradient rank, and (ii) principal channel filtering, which removes task-irrelevant channels, enabling the one-step spectral initialization gradient to better align with the long-horizon optimization trajectory. Extensive experiments demonstrate that our method consistently improves both convergence speed and final performance across multiple diffusion fine-tuning benchmarks, including subject-driven generation, controllable generation, and deblurring, achieving not only performance improvement but also earlier stages of convergence over baseline LoRA and other spectral-init methods.

Jiayang Gu, Zheng Fang, Lichaun Xiang +3

University of Warwick · Bytedance

Flow Matching Diffusion Model Fine-Tuning Low-Rank Adaptation Spectral Methods

Sep 14, 2026cs.LG

Refinement-based Flow Policy Optimization

Flow-based policies offer an expressive representation for online reinforcement learning, but conventional flow matching requires samples drawn from the distribution to be modeled. This poses a challenge when the desired action distribution is defined only implicitly by a Q-function, since directly sampling actions from the resulting distribution is generally intractable. We propose Refinement-Based Flow Policy Optimization (RFPO), a novel framework for training a flow policy in online reinforcement learning by alternating between Q-guided sample refinement and self-target flow matching. RFPO first generates actions from Gaussian noise using the current flow policy and then uses a finite-step stochastic refinement procedure to move them toward an energy-based distribution induced by the Q-function. Each refined action is then paired with its corresponding initial noise sample and used as a fixed target for flow-matching training. By repeatedly refining its own outputs and learning from the resulting targets, RFPO incorporates Q-guidance into the policy without requiring direct samples from the target distribution, while retaining the capacity to represent multiple action modes. We further provide a theoretical analysis of the distributional dynamics induced by RFPO. Across six continuous-control tasks, RFPO matches or outperforms a standard Gaussian-policy baseline on almost every task. Experiments on six synthetic two-dimensional target distributions with diverse geometries demonstrate that RFPO captures complex multimodal structure without mode collapse.

Bumgeun Park, Hyukjun Yang, Donghwan Lee

Korea Advanced Institute of Science and Technology (KAIST)

RL Control Flow Matching Policy Optimization Continuous Control

Sep 14, 2026cs.LG

Branched Optimal Transport Amortization

Methods of Branched Optimal Transport (BOT) mimic the economy and efficiency of natural tree-like structures, such as those found in rivers and biological systems. These methods are widely applicable for designing efficient networks in society, from river basins and blood vessels to mail and gas distribution systems. However, they remain understudied in the context of designing deep generative models, particularly at a large scale. Standard continuous-time generative models, such as the flow matching approach, fail to capture the inherent hierarchical and branching patterns present in real-world data. Current models provide no mechanism for flows to merge or share pathways to minimize total transport cost. Inspired by the "economy of scale" principle in BOT, we introduce a novel, scalable branched flow-matching algorithm designed to solve the branched optimal transport problem in high dimensions. Our method adapts the Benamou-Brenier continuous-time optimal transport formulation to learn branched generative flows. These flows allow probability mass to aggregate along common pathways before branching out to diverse targets. Parametrized by neural networks, our method effectively learns complex branched generative processes. We demonstrate its effectiveness on challenging high-dimensional tasks in biology and image generation.

Semyon Semenov, Viktor Kovalchuk, Meir Roketlishvili +4

MBZUAI

Flow Matching Generative Modeling Flow-Based Generative Modeling Optimal Transport

Sep 12, 2026cs.LG

CyFM: Cylindrical Optimal Transport for Few-Step Complex-Valued Flow Matching

Complex-valued signals like MRI and audio spectrograms are typically modelled as flat two-channel Euclidean data. The inherited Euclidean metric

dA^2 + A^2 dθ^2

vanishes at the origin, leaving phase unpenalised exactly where the signal is weakest. We replace it with the decoupled product metric

dA^2 + dθ^2

on the cylindrical closure

[0, \infty) \times S^1

, which stays non-degenerate at

A = 0

. We measure what this substitution costs and buys. Exact analytical bridges across synthetic fields, fastMRI knee data, and LibriSpeech spectrograms show Cartesian paths induce a heavy-tailed angular velocity distribution (Pareto index

\approx 1

). Under independent coupling, 43%-49% of signal energy falls on paths turning faster than

π

rad per unit time. Cylindrical paths never reach this speed. We formulate Cylindrical Flow Matching (CyFM) to strictly bound the angular regression target, coupling noise and data via exact minibatch Optimal Transport jointly over whole fields. This coupling reduces few-step generation error by 3%-60%. CyFM achieves lower generative error than the best Cartesian baseline at every step up to

k = 8

on synthetic fields and speech spectrograms, with all seeds separated. On knee MRI, the single-step advantage is 1.8x. At convergence (

k = 100

), the two geometries show no significant difference. Finally, a prior-only control exposes the cost of flat parametrisation: on synthetic fields, a single Cartesian Euler step performs worse than the unintegrated noise prior (0.376 vs. 0.150).

Marcel Musiałek, Iga Wolanin, Damian Ryczko +2

Wrocław University of Science and Technology Wrocław, Poland

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

Sep 12, 2026cs.LG

Model-Aware Schedules Improve Generation via Fiberwise Optimal Transport

Diffusion and flow-matching schedules control the signal and noise coefficients that mix data and noise along affine probability paths. Minimizing a kinetic action defined on coefficient paths, motivated by optimal transport, helps explain strong baselines but remains model-agnostic and ignores prediction error. Here we introduce a model-aware schedule construction based on fiberwise optimal transport. At a fixed time and state on the probability path, compatible signal/noise decompositions form an affine fiber. We define a fiberwise prediction risk by averaging optimal-transport costs between the true and predictor-induced decompositions within these fibers. On a fixed coefficient curve, combining this risk with coefficient-path kinetic action yields a closed-form optimal time allocation. This construction extends to general linear prediction targets, and the risk profile can be estimated from an early baseline checkpoint. We evaluate DDPMs and flow matching across prediction targets, training configurations, risk-estimation checkpoints, datasets, and architectures. Our model-aware schedules consistently outperform strong baselines, including a 38.6% relative FID reduction for flow matching on CIFAR-10 at 16 function evaluations. Each model-agnostic kinetic baseline determines its own kinetic reference coordinate. In these coordinates, fiberwise-risk profiles from independently trained models in different settings align closely after normalization to unit area. The resulting schedule deformations used in training also align, suggesting empirical universality across the evaluated models and settings. Pretrained-checkpoint diagnostics extend this normalized-risk agreement to larger conditional latent diffusion and 2-RF models. A frozen analytic allocation template retains most of the model-aware improvement without further risk estimation or model-specific fitting.

Luyi Jia, Boyan Zhang, Yilun Liu +1

Arnold-Sommerfeld-Center for Theoretical Physics, Ludwig-Maximilians-Universität München, Munich, Germany · Institute of Informatics, Ludwig-Maximilians-Universität München, Munich, Germany · Munich Center for Machine Learning, Munich, Germany

Flow Matching Diffusion Timestep Scheduling Flow-Based Generative Modeling Optimal Transport Diffusion Models

Sep 11, 2026cs.LG

Flow Duality and Source Geometry for Categorical Generation

Continuous and discrete flow matching are usually treated as separate constructions. This paper identifies a duality between them: projecting continuous convex-interpolant paths with one-hot targets through a position-wise argmax yields discrete convex-interpolant paths. The result requires source laws with appropriate coordinate symmetry and boundary regularity, and it makes the continuous source distribution an explicit design choice for categorical generation. We derive the induced discrete interpolation behavior for Gaussian, bounded-uniform, and centered negative-exponential sources, showing that different source geometries lead to qualitatively different transition timing and vocabulary-size dependence. Small visual diagnostics and a short language-modeling pilot suggest that these source-design effects can also appear in learned transports and early generative quality.

Etrit Haxholli

Flow Matching Flow-Based Generative Modeling Discrete Flow Matching

Sep 9, 2026cs.RO

Frequency-Conditioned Flow Matching for Vision-Language-Action Models

Robot actions are temporally correlated trajectories whose frequency components encode motion at different scales with highly non-uniform energy distributions. Yet Flow Matching--based vision-language-action (VLA) models typically generate actions in temporal coordinates, without explicitly modeling or systematically leveraging this frequency heterogeneity. We introduce \emph{FreqFM}, a frequency-conditioned Flow Matching framework for VLA models. It raises action frequency from an implicit trajectory property to an explicit conditioning dimension that spans the entire generation pipeline. Concretely, in DCT frequency coordinates, FreqFM constructs a spectrum-matched source distribution, adaptively balances the objective across frequencies, and constrains per-frequency guidance residuals using the corresponding reference transport scales. FreqFM integrates into existing Flow Matching action experts without changing the VLA backbone. Across LIBERO, LIBERO-Plus, and VLA-Arena, FreqFM consistently improves performance, including a 9.3-point gain on LIBERO-Plus, and further demonstrates its effectiveness on six real-robot tasks.

Haochen Niu, Shengye Dong, Hao Liu +2

AGIBOT · Xi’an Jiaotong University

Flow Matching Robot Motion Generation Vision-Language-Action Models

Sep 9, 2026stat.ML

FlowCPO: A Unified Divergence View of Preference Alignment for Flow Models

Preference alignment for flow and diffusion models now spans online reinforcement learning and offline preference optimization, but the relation between these methods remains unclear. In particular, existing forward-process alignment methods require fresh samples from the current model, while offline methods based on fixed preference pairs rely primarily on positive-only fine-tuning or DPO-style likelihood-ratio surrogates. We organize these approaches through a divergence-based framework and introduce FlowCPO, an offline forward-KL objective that uses both preferred and dispreferred samples without online rollouts. For linear interpolation, we show under explicit regularity conditions that the forward-KL objective is bounded by a contrastive flow matching loss, yielding a tractable surrogate on fixed data. We further show that this loss is nonnegative, whereas the signed regression loss of simplified FlowDPO can be unbounded below. In the in-domain setting, FlowCPO achieves higher mean GenEval and OCR scores than the evaluated baselines, reaching 0.84 and 0.87 versus 0.81 and 0.74 for FlowDPO at CFG 3.0. In the out-of-domain setting, the results are mixed, with the best GenEval result but lower reward scores than RFT on several metrics.

Yansen Han, Shengyi Liao, Peng Sun +4

Westlake University · Zhejiang University · Kling Team, Kuaishou Technology

Pairwise Preference Learning Flow Matching Flow-Based Generative Modeling Preference Alignment Offline Preference Optimization

Sep 7, 2026cs.CV

Latent-to-Latent Flow for Volumetric Stochastic Segmentation

Uncertainty arising from inter-observer variability in medical image segmentation plays an important role in developing treatment plans. Research in this area is inhibited by the lack of multiple annotations for large-scale medical datasets, especially for volumetric data, which suffers from additional scaling and computational complexity challenges. Flow matching has emerged as a powerful framework for generative modelling and has also been demonstrated to maintain strong performance when working with latent representations of images. In this work, we introduce a latent-to-latent flow technique for stochastic segmentation of medical volumes via encoded representations of both the image and label space. We evaluate our method on two challenging applications covering delineation uncertainty for radiotherapy planning and multiple organ structure segmentation, improving efficiency up to 14x compared with full resolution models while maintaining clinically relevant performance.

Omar Todd, Sooha Kim, Raghav Mehta +5

Imperial College London, UK · The Royal Marsden Hospital, London, UK · Imperial College Healthcare NHS Trust, London, UK

Flow Matching Medical Image Segmentation 3D Medical Image Segmentation Segmentation Uncertainty Estimation

Sep 7, 2026cs.LG

PCFlow: Physics-Conditioned Flow Matching for GPR B-Scan Image Synthesis

Ground-penetrating radar (GPR) B-scan image synthesis is important for data augmentation, algorithm validation, and simulation acceleration, yet generating radargrams with both visual realism and physical consistency remains challenging. Existing learning-based generative models often emphasize visual appearance but provide limited control over response geometry. In this paper, we propose PCFlow, a physics-conditioned flow matching framework for fast GPR B-scan image synthesis. The core of PCFlow is a Maxwell-informed dense physical condition field constructed from the parameterized physical model used for electromagnetic simulation, including material properties, target geometry, propagation cues, and response-domain priors. This condition field provides an interpretable interface between physical scene parameters and radar response geometry, and guides conditional flow matching in the VAE latent space toward physically feasible generation paths. We evaluate PCFlow on a gprMax-based buried-pipeline dataset with both in-distribution and out-of-distribution test cases. Experimental results show that PCFlow generates images with more accurate response geometry and high visual fidelity, demonstrating its effectiveness for controllable and physically faithful radar image synthesis.

Zhijie Shen, Chenchen Fu, Xuanhao Chang +2

College of Computer Science and Technology, Jilin University, Changchun 130012, China · Symbol Computation and Knowledge Engineering of the Ministry of Education, Jilin University, Changchun 130012, China

Flow Matching Conditional Image Generation Remote Sensing Physics-Informed ML

Sep 7, 2026cs.AI

MedFlow: Class-Aware Multi-Scale Generation for Medical Time-Series Synthesis

Synthetic medical time-series generation can alleviate data scarcity and support the development of reliable clinical prediction models. However, existing methods mainly focus on matching the overall distribution and temporal dynamics of real data, which does not necessarily ensure strong downstream utility on imbalanced medical datasets. Clinically informative patterns often occur at heterogeneous temporal scales, while rare minority-class characteristics can be obscured by dominant population patterns. To address these challenges, we propose MedFlow, a class-aware multi-scale flow matching framework for medical time-series synthesis. MedFlow employs a vector-quantized multi-scale tokenizer to represent medical sequences at complementary temporal resolutions, capturing both coarse clinical trends and fine-grained dynamics. We further introduce Token Marginal Guidance, which incorporates class-conditional token statistics directly into the flow matching process to steer generation toward class-specific regions of the learned tokens. This mechanism strengthens minority-class patterns, while preserving the global and tail distributions of real data. Experiments on four public datasets covering electronic health records, EEG, and ECG signals demonstrate that MedFlow consistently outperforms recent state-of-the-art diffusion-based baselines across downstream prediction tasks. On average, it improves AUPRC by 5.8%, reduces Context-FID by 88.6%, and achieves 3.8

\times

higher sampling throughput.

Yanhao Huang, Shibo Feng, Wanjin Feng +2

Shanghai Jiao Tong University · Nanyang Technological University · Tsinghua University

Flow Matching Synthetic Data Generation Time Series Generation Conditional Generative Modeling