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.

Jul 13Week of Sep 28

Latest papers 446

May 21, 2026cs.CV

RiT: Vanilla Diffusion Transformers Suffice in Representation Space

Flow matching with

x

-prediction -- regressing the clean data point rather than the ambient velocity -- is known to exploit low-dimensional manifold structure effectively in pixel space \cite{li2025back}. We ask whether a pretrained representation space, while containing a low-dimensional data manifold of comparable intrinsic dimensionality, offers a distribution more favorable for flow-matching learning. Comparing pixel, SD-VAE, and DINOv2 features along four geometric axes, we find that pixel and DINOv2 share nearly identical intrinsic dimensionalities (both

\hat{d}\!\approx\!33

) yet DINOv2 exhibits

7.3\times

higher effective rank,

35\times

better covariance conditioning,

11.5\times

lower excess kurtosis, and

1.7\times

lower on-manifold interpolation error; SD-VAE latents are consistently intermediate, indicating that the advantage stems from representation-learning objectives rather than mere compression. These statistical properties render the flow-matching regression well-conditioned and remove the need for the specialized prediction heads or Riemannian transport used by prior DINOv2 diffusion methods. We propose the \emph{Representation Image Transformer} (RiT): a vanilla Diffusion Transformer trained by

x

-prediction on frozen DINOv2 features, augmented only by a dimension-aware noise schedule and joint \texttt{[CLS]}-patch modeling. On ImageNet

256{\times}256

, RiT attains FID 1.45 without guidance and 1.14 with classifier-free guidance, outperforming DiT

^\text{DH}

-XL with

19\%

fewer parameters (676M vs.\ 839M). The resulting ODE is efficiently solvable at coarse discretizations: with classifier-free guidance,

5

Heun steps already reach FID 2.0 and

10

steps reach 1.25, without distillation or consistency training. Code at https://github.com/lezhang7/RiT.

Le Zhang, Ning Mang, Aishwarya Agrawal

Mila – Québec AI Institute, UdeM · Utrecht University · Canada CIFAR AI Chair

Flow Matching Visual Representation Learning Diffusion Transformer Diffusion-Based Image Generation Diffusion Models

May 21, 2026q-bio.PE

PhylaFlow: Hybrid Flow Matching in Billera-Holmes-Vogtmann Tree Space for Phylogenetic Inference

Phylogenetic trees are hybrid objects: branch lengths vary continuously, while topologies change discretely through edge contractions and expansions. Billera-Holmes-Vogtmann (BHV) tree space provides a canonical geometry for this structure, representing each resolved topology as a Euclidean orthant and topological changes as motion across shared lower-dimensional boundaries. We introduce PhylaFlow, a hybrid flow-matching model that learns posterior-basin transport in BHV tree space. PhylaFlow is trained on BHV geodesic paths from random starting trees to short-run posterior samples, coupling continuous branch-length motion within orthants with learned boundary events and discrete topology transitions. We evaluate the learned geometry operationally: if the flow reaches posterior-relevant regions, finite-budget Bayesian refinement initialized from, or guided by, its terminal trees should recover posterior-supported topologies more efficiently. Across DS1-DS8 phylogenetic posterior benchmarks, PhylaFlow substantially reduces initial Tree-KL relative to classical initializers. After finite-budget MrBayes refinement, direct PhylaFlow improves early and intermediate topology-recovery trajectories on most datasets, while split-guided PhylaFlow-MCMC obtains the strongest hard-case results. The best PhylaFlow variant outperforms short-warmup on seven of eight datasets and PhyloGFN on five of eight under the same refinement budget. In a joint sequence-conditioned experiment, sequence embeddings steer posterior split recovery, although exact posterior topology recovery remains preliminary. These results show that hybrid flow matching can learn actionable transport in BHV tree space and provide a geometry-aware proposal mechanism for Bayesian phylogenetic inference.

Yasha Ektefaie, Leo Cui, Shrey Jain +2

Eric and Wendy Schmidt Center, Broad Institute of MIT and Harvard · Department of Biomedical Informatics, Harvard Medical School · Centennial High School +1

Flow Matching Tree Search Bayesian Inference Posterior Sampling Phylogenetic Inference

May 20, 2026cs.CV

Linear-DPO: Linear Direct Preference Optimization for Diffusion and Flow-Matching Generative Models

Direct Preference Optimization (DPO) is successful for alignment in LLMs but still faces challenges in text-to-image generation. Existing studies are confined to denoising diffusion models while overlooking flow-matching, and suffer from an objective mismatch when applying discrete NLP-based DPO to regression-based generative tasks.\ In this paper, we derive a generalized DPO objective that covers both diffusion and flow-matching via a unified reverse-time SDE framework, and point out from a gradient perspective that the standard DPO objective is suboptimal for text-to-image generation. Consequently, we propose Linear-DPO, which replaces the aggressive sigmoid-based utility function with a sustained linear utility and incorporates an EMA-updated reference model. Qualitative and quantitative experiments on diffusion models (SD1.5, SDXL) and flow-matching model (SD3-Medium) demonstrate the superiority of our approach over existing baselines.

Kesong Li, Yixuan Xu, Kuo-kun Tseng +3

School of Computer Science and Technology, Harbin Institute of Technology, Shenzhen, China · Alibaba Group, Hangzhou, Zhejiang, China

Diffusion Model Alignment Flow Matching Direct Preference Optimization T2I Generation

May 19, 2026cs.CV

FullFlow: Upgrading Text-to-Image Flow Matching Models for Bidirectional Vision--Language Generation

Modern text-to-image diffusion models encode rich visual priors, but expose them only through one-way text-conditioned generation. Existing unified vision--language models derived from them recover bidirectional capability through large-scale joint pretraining or substantial retraining of the text pathway, discarding the strong image prior the text-to-image backbone already encodes. We introduce \emph{FullFlow}, a parameter-efficient recipe that upgrades a pretrained rectified-flow text-to-image model into a bidirectional vision--language generator by training only LoRA adapters and lightweight text heads. FullFlow keeps images in their native continuous flow and adds a discrete insertion process for text. Separate image and text timesteps turn inference into trajectory selection in a two-dimensional generative space, enabling text

\rightarrow

image, image

\rightarrow

text, joint sampling, and partial-text prediction with a single backbone. On Stable Diffusion 3 (SD3) under an identical trainable-parameter count and matched LoRA rank, FullFlow improves text

\rightarrow

image FID from

62.7

to

31.6

and image

\rightarrow

text CIDEr from

2.0

to

99.4

over a LoRA equivalent following the previous SOTA formulation (Dual Diffusion) at matched wall-clock training time, while reducing peak VRAM from

{\sim}84

,GB to

{\sim}38

,GB and raising throughput by

{\sim}8\times

on two RTX A5000 GPUs in under 24 hours, training only

{\sim}5\%

of the backbone parameters. The same recipe transfers to FLUX.1-dev and supports downstream VQA through partial-text generation. These results show that strong bidirectional vision--language capability can be unlocked from pretrained text-to-image flow models without full multimodal pretraining.

Eric Tillmann Bill, Enis Simsar, Alessio Tonioni +1

ETH Zurich · Google

Flow Matching Image Captioning Vision-Language Models VLM Adaptation Flow-Based Generative Modeling T2I Diffusion Models

May 19, 2026stat.ML

Tail Annealing for Heavy-Tailed Flow Matching

Standard generative models struggle with heavy-tailed data: Lipschitz architectures cannot produce power-law tails from Gaussian noise, and interpolating between heavy-tailed data and Gaussians is ill-posed. We propose a simple fix: apply the soft-log transform

φ(x) = \mathrm{sign}(x) \cdot \log(1 + |x|)

coordinate-wise to data before training, then exponentiate samples after generation. A Hill diagnostic decides per-coordinate whether to transform, leaving light-tailed margins untouched at no added complexity. This compresses heavy tails into a range where standard flow matching succeeds, without heavy-tailed base distributions or architectural modifications. We provide theoretical intuition for why this works: the log-transform maps Pareto tails to exponentials, and the induced dynamics implement a form of tail annealing via power transformations. On a 144-configuration multivariate benchmark (3 copulas,

d

up to 100, 4 tail indices), Log-FM dominates specialized baselines on

W_1

, CVaR

_{99}

, and extreme-quantile metrics, and is the only method with zero severe divergences across 2{,}880 runs.

Jean Pachebat

1CMAP, Ecole Polytechnique, Institut Polytechnique de Paris, France.

Flow Matching Generative Modeling Flow-Based Generative Modeling Heavy-Tailed Distributions

May 19, 2026cs.CV

FlowErase-RL: Rethinking Concept Erasure as Reward Optimization in Flow Matching Models

Recent advances in flow matching models have significantly improved text-to-image generation quality, but also introduce growing safety risks due to the generation of harmful or undesirable content. Existing concept erasure methods are either inference-time interventions with limited effectiveness or rely on supervised fine-tuning (SFT), which requires precisely aligned data and struggles with scalability and multi-concept settings. In this paper, we propose \emph{FlowErase-RL}, the first GRPO-based framework for concept erasure in flow matching models. We reformulate concept erasure as a reward optimization problem and introduce a \textbf{dynamic dual-path reward mechanism} that jointly optimizes (i) a Concept Erasure (CE) reward to suppress target concepts and (ii) a Non-target Space (NS) reward to preserve generative fidelity. The two reward paths are adaptively balanced during training via a performance-driven switching strategy, enabling stable optimization without explicit supervision. Extensive experiments on nudity, object, and artistic style erasure demonstrate that our method achieves state-of-the-art erasure performance while maintaining strong image quality and semantic alignment. Moreover, it exhibits robust resistance to adversarial attacks and scales effectively to multi-concept scenarios. Our results establish a new paradigm for safe and controllable generation in flow matching models.

Yi Sun, Zhiqi Zhang, Xinhao Zhong +5

Harbin Institute of Technology, Shenzhen · Jilin University · Tsinghua Shenzhen International Graduate School, Tsinghua University +2

Flow Matching T2I Generation Safe T2I Generation Flow-Based Generative Modeling RL for Generative Models Concept Erasure

May 19, 2026cs.CV

Multi-Scale Generative Modeling with Heat Dissipation Flow Matching

Diffusion models are widely used in image generation, with most relying on noise-based corruption and denoising. A distinct branch instead uses blur as the main corruption, preserving better color budgets and multi-scale detail by providing multi-scale priors. However, blur-based models remain in SDE-based frameworks and are not integrated into ODE-based frameworks, such as Flow Matching (FM). Meanwhile, in the blur-based formulation, the classical inverse heat-dissipation (IHD) process faces an ill-posed challenge. Moreover, under the data-manifold assumption, regressing blurred images from high-dimensional noise (or velocity) space is also difficult. We propose Heat Dissipation Flow Matching (HDFM), which introduces a continuous blurred (heat-dissipation) process into FM to inject multi-scale priors. HDFM aligns an interpolated heat-dissipation path to address ill-posedness and adopts

x

-prediction to mitigate high-dimensional regression difficulty. Toy experiments and ablation studies show that HDFM consistently benefits from both blur and

x

-prediction. The performance of HDFM outperforms most baseline methods on all datasets.

Jun Ma, Hanquan Zhang, Yanjun Qin +2

Department of Systems Science, Faculty of Arts and Sciences, Beijing Normal University, Zhuhai 519087, China · School of Computer Science and Technology, Xinjiang University, Urumqi 830049, China · International Academic Center of Complex Systems, Beijing Normal University, Zhuhai 519087, China +1

Flow Matching Image Generation Generative Modeling Flow-Based Generative Modeling Diffusion Models

May 19, 2026cs.GR

Matérn Noise for Triangulation-Agnostic Flow Matching on Meshes

This paper tackles the task of learning to generate signals over triangle meshes in a triangulation-agnostic manner, meaning the trained model can be applied to different meshes and triangulations effectively. Practically, the paper adapts the flow matching (FM) paradigm to a mesh-based, triangulation-agnostic setting. Theoretically, it proposes a specific noise distribution which is triangulation agnostic, to be used inside the FM model's denoising process. While noise distributions are usually trivial to devise for, e.g., images, devising a triangulation-agnostic distribution proves to be a much more difficult task. We formulate a mathematical definition of triangulation agnosticism of distributions, via their spectrum. We then show that a discretization of a specific Gaussian random field called a Matérn process holds these desired properties, and provides a simple and efficient sampling algorithm. We use it as our noise model, and adapt FM to the triangulation-agnostic setting by using a state-of-the-art approach for learning signals on meshes in the gradient domain -- PoissonNet -- as the denoiser. We conduct experiments on elaborate tasks such as sampling elastic rest states, and generating poses of humanoids. Our method is shown to be capable of producing highly realistic results for meshes of over one million triangles, significantly exceeding the state-of-the-art in quality and diversity.

Tianshu Kuai, Arman Maesumi, Daniel Ritchie +1

Université de Montréal & Mila, Canada · Brown University, USA

Flow Matching 3D Mesh Generation Generative Modeling Flow-Based Generative Modeling

May 18, 2026cs.CV

StableHand: Quality-Aware Flow Matching for World-Space Dual-Hand Motion Estimation from Egocentric Video

Recovering world space 4D motion of two interacting hands from egocentric video is a fundamental capability for supervising robot policy learning, where wrist trajectories track the end-effector and finger articulations specify the grasp pose. Two major challenges arise in this setting: hands frequently leave the camera view for extended periods due to head motion, and persistent hand-object interactions cause severe occlusions of one or both hands. Existing methods uniformly condition on noisy hand motion observations without accounting for their per-frame reliability, leading to substantial performance degradation. Our key insight is that accurate world space hand motion estimation is tightly coupled with the quality of per-frame hand observations. To this end, we decompose the quality of hand motion observations extracted from an off-the-shelf hand pose estimator into four channels: wrist global translation and finger articulations for both hands. We propose StableHand, a quality-aware flow-matching framework conditioned on these four-channel quality signals, which are predicted by a learned quality network. We naturally incorporate the quality signals into the flow-matching process through a per-channel forward schedule, a quality-adjusted velocity target, AdaLN modulation of the DiT denoiser, and a quality-aware ODE initialization. This unified generative process preserves high-quality observations while reconstructing unreliable ones using a learned bimanual motion prior. Experiments on HOT3D and ARCTIC, two egocentric benchmarks featuring long missing-hand spans and persistent hand-object occlusions, show that StableHand achieves state-of-the-art performance across all reported metrics, reducing W-MPJPE by 20-25% compared to the strongest baseline, with the largest gains on heavily occluded ARCTIC sequences.

Huajian Zeng, Chaohua Yao, Yuantai Zhang +3

Mohamed bin Zayed University of Artificial Intelligence · University of Illinois at Urbana-Champaign · Imperial College London

Flow Matching 3D Hand Pose Estimation Egocentric Video Understanding

May 18, 2026stat.ML

Flowing with Confidence

Generative models can produce nonsensical text, unrealistic images, and unstable materials faster than simulation or human review can absorb; without per-sample confidence, trust erodes. Existing fixes run

k

ensembles or stochastic trajectories at

k\times

compute, measuring variability between models, not model confidence. We propose Flow Matching with Confidence (FMwC). FMwC injects input-dependent multiplicative noise at selected layers, propagates its variance through the network in closed form, and integrates it along the ODE trajectory, yielding a per-sample confidence score at standard sampling cost. The score supports multiple uses: filtering improves image quality and thermodynamic stability of crystals; editing rewinds trajectories to the points where the model commits and redirects them; and adaptive stepping concentrates ODE compute where the flow is ambiguous. We find that the confidence score correlates with the magnitude of the divergence of the learned velocity field, which gives us a window to understand the generative process, opening up surgical forms of guidance that target the moments that matter, new sampling algorithms and interpretability of generative models.

Friso de Kruiff, Dario Coscia, Max Welling +1

CuspAI · AMLab, University of Amsterdam · mathLab, SISSA

Flow Matching Uncertainty Quantification Image Generation Generative Modeling Flow-Based Generative Modeling

May 18, 2026cs.CV

Stabilizing, Scaling & Enhancing MeanFlow for Large-scale Diffusion Distillation

Diffusion models exhibit remarkable generative capability, but their high latency limits practical deployment. Many studies have attempted to reduce sampling steps to accelerate inference. Among them, MeanFlow has attracted considerable attention due to its concise formulation and remarkable performance. Nevertheless, the instability of its optimization objective and the ''mean-seeking bias'' have limited its applicability to distill large-scale industrial models. To stabilize MeanFlow for distilling large-scale models, we first introduce a warm-up technique, in which the original differential solution of MeanFlow is replaced by a discrete solution. This design avoids training collapse caused by the MeanFlow target containing a stop-gradient term from an undertrained model. Once the model acquires a preliminary ability to fit the average velocity field, we switch the optimization objective back to the differential solution, enabling further refinement. Meanwhile, to alleviate the ''mean-seeking bias'' of MeanFlow under extremely few-step inference with complex target distributions, we incorporate trajectory distribution alignment as an auxiliary objective, encouraging the student model's trajectory distribution to align more closely with that of the teacher model. Our proposed distillation framework achieves superior performance compared to existing distillation approaches when applied to the text-to-image (T2I) model FLUX.1-dev (up to 12B parameters). Furthermore, when extended to the 80B-parameter state-of-the-art (SOTA) T2I model HunyuanImage 3.0, our method continues to demonstrate robust generalization and strong performance.

Xiao He, Yang Li, Peizhen Zhang +3

1State Key Laboratory of Integrated Services Networks, Xidian University · 2Tencent Hunyuan

Flow Matching Diffusion Model Distillation MeanFlow Few-Step Diffusion Sampling Mean Flow T2I Diffusion Models

May 17, 2026cs.LG

Drift Flow Matching

Iterative generative models such as Flow Matching and Diffusion models have demonstrated strong test-time scaling behavior, where additional inference computation can improve generation quality. In contrast, Drift Models offer efficient one-step generation, but their direct generation paradigm limits such flexibility. In this work, we propose Drift Flow Matching (DFM), a framework that connects drifting generative modeling with flow-based iterative generation. DFM preserves the efficiency of direct transport maps while enabling generation to be refined through multiple inference steps when desired. This bridges the gap between one-step Drift Models and multi-step Flow Matching methods, and provides a novel generative paradigm that can adapt sampling computation to different quality--efficiency requirements. Extensive experiments across different tasks and datasets demonstrate the effectiveness and generality of the proposed framework.

Chenrui Ma, Xi Xiao, Lin Zhao +3

University of California, Irvine · University of Virginia · University of Alabama at Birmingham +1

Flow Matching Inference-Time Scaling One-Step Generative Modeling Flow-Based Generative Modeling Drifting Models

May 16, 2026cs.CE

Weighted Flow Matching and Physics-Informed Nonlinear Filtering for Parameter Estimation in Digital Twins

Digital twins (DTs) rely on continuous synchronization between physical systems and their virtual counterparts through online parameter estimation under uncertainty. In many practical settings, however, this task is challenged by low observability, weak excitation, nonlinear dynamics, and noisy or biased measurements. In this work, we develop a new mathematical framework that integrates Weighted Flow Matching (WFM) generative modeling with physics-informed nonlinear filtering to enhance parameter estimation in DTs. WFM relies on dynamic reweighting of training samples, which guides the generative model toward parameter regimes most informative of the evolving system state. This generative component is tightly coupled with a physics-informed filtering architecture based on the Unscented Kalman Filter (UKF), yielding a unified DT framework that combines data-driven probability transport with physically consistent state and parameter estimation. The effectiveness of the new integrated framework is demonstrated within a spacecraft DT architecture, where stable moment of inertia estimation is achieved under uncertain and noisy sensing, with significant performance improvements over established approaches such as Extended Kalman Filtering (EKF) and Ensemble Kalman Filtering (EnKF). These results highlight the potential of weighted generative modeling as a core mechanism for real-time DT synchronization in operational and mission-critical systems.

Yasar Yanik, Himadri Basu, Ricardo G. Sanfelice +1

Department of Applied Mathematics, University of California, Santa Cruz, CA 95064, USA · Department of Electrical and Computer Engineering, University of California, Santa Cruz, CA 95064, USA

Flow Matching Kalman Filtering Unscented Kalman Filtering Physics-Informed ML Digital Twins

May 16, 2026cs.LG

Learning Unbiased Permutations via Flow Matching

Learning permutations is fundamental to sorting, ranking, and matching, but existing differentiable methods based on entropy-regularized Sinkhorn produce a single softened solution and collapse under ambiguity. We present PermFlow, a conditional flow matching framework that operates directly on the affine subspace of matrices with unit row and column sums. A closed-form tangent-space projector preserves these constraints exactly along every trajectory, by construction rather than through iterative correction, and a nearest-target coupling routes distinct noisy initializations toward distinct valid permutations. The result is a model that captures multimodal permutation distributions rather than collapsing them to a single mode. On a visual sorting task with blended-digit ambiguity and a symmetric linear assignment problem, PermFlow achieves high accuracy on unambiguous inputs and recovers both valid permutations under ambiguity, where Sinkhorn-based baselines structurally fail.

Yimeng Min, Carla P. Gomes

Department of Computer Science Cornell University Ithaca, NY, USA

Flow Matching Combinatorial Optimization Flow-Based Generative Modeling

May 15, 2026cs.LG

Wavelet Flow Matching for Multi-Scale Physics Emulation

Accurate emulation of multi-scale physical systems governed by PDEs demands models that remain stable over long autoregressive rollouts while preserving fine-scale structures. Deterministic emulators produce overly-smoothed predictions, while generative approaches better capture details but are costly. Latent-space generative models have emerged as a compromise but with the additional cost of separately pre-trained autoencoders. We propose Wavelet Flow Matching (WFM), a novel generative emulator that overcomes current trade-offs between cost and skill by performing optimal-transport directly in the multi-scale wavelet space. Rather than learning a latent compression, WFM leverages the hierarchical structure of a U-Net to jointly predict transport velocities of a prescribed wavelet representation. On three challenging systems of chaotic fluid dynamics, WFM achieves superior long-horizon stability, accuracy and spectral coherence compared to state-of-the-art models. Our results clearly position the wavelet space as an effective training-free representation for generative emulation of complex physical dynamics.

Gabriele Accarino, Juan Nathaniel, Carla Roesch +4

Department of Earth and Environmental Engineering Columbia University, NY, USA · University of Edinburgh Edinburgh, Scotland, UK · Courant Institute of Mathematical Sciences New York University, NY, USA +2

Flow Matching PDE Surrogate Modeling Wavelet Methods Generative Modeling Flow-Based Generative Modeling Computational Fluid Dynamics

May 15, 2026cs.LG

Multiscale Supervised Unbalanced Optimal Transport Flow Matching

Unbalanced optimal transport (UOT) provides a principled framework for modeling single-cell transitions and birth-death dynamics, but its high computational cost limits scalability to large-scale datasets. Although single-cell data often contain hierarchical annotations and known transition priors, existing UOT approximations rarely exploit this multiscale structure or prior knowledge. We introduce Multiscale Supervised Unbalanced Optimal Transport Flow Matching (MUST-FM), a simulation-free framework that scales UOT by leveraging hierarchical data structure. MUST-FM further supports an optional supervised formulation that incorporates transition priors, such as cell lineages, to guide the learning of displacement fields and mass variations. Experiments show that MUST-FM reduces computational overhead while achieving robust and biologically meaningful trajectory inference, enabling dynamic modeling of atlas-scale single-cell datasets.

Qiangwei Peng, Lezhi Chen, Peijie Zhou

College of Electrical Engineering Sichuan University, Sichuan, China · AI for Science Institute, Beijing, China

Flow Matching Single-Cell Transcriptomics Optimal Transport

May 15, 2026cs.LG

Entropy Across the Bridge: Conditional-Marginal Discretization for Flow and Schrödinger Samplers

For a fixed flow-based generative model under a small inference budget, sample quality can depend strongly on where the sampler spends its few function evaluations. Flow matching and Schrödinger bridges define probability paths, yet their inference grids are usually heuristic or inherited from one-endpoint diffusion. We derive a conditional-marginal entropy-rate objective for bridge-aware discretization, separating endpoint-conditioned bridge geometry from marginal flow evolution, and use it to build a training-free entropic inference-time scheduler from first principles. For Gaussian Brownian bridges this rate is closed-form and U-shaped, motivating boundary-heavy nonuniform grids. On trained two-dimensional bridge/flow models, the estimated profile recovers the predicted shape and improves 10-step ODE-Heun MMD over linear by 18.1%, with a paired 22.7% SDE-Heun improvement in the same low-NFE sweep. On EDM/CIFAR-10, the entropic time-discretization gives the best tested five-step FID (186.3 \pm 4.0 versus 200.5 \pm 2.9 for linear and 238.0 \pm 5.3 for cosine). On AlphaFlow protein generation, entropic conditional-marginal (cond-marg) scheduling shows advantage in low-NFE regimes on both CAMEO22 and ATLAS benchmarks. These results support entropy-rate scheduling as a practical low-budget allocation signal for high-dimensional bridge and flow samplers.

Bruno Trentini, Dejan Stancevic, Michael M. Bronstein +2

NVIDIA Corporation, Santa Clara, CA, USA · University of Oxford, Dept. of Computer Science, Oxford, UK · Donders Institute for Brain, Cognition, and Behaviour, Radboud University, Nijmegen, NL +1

Flow Matching Schrödinger Bridges Few-Step Diffusion Sampling Adaptive Sampling Flow-Based Generative Modeling Diffusion Model Inference Acceleration

May 15, 2026cs.RO

FocalPolicy: Frequency-Optimized Chunking and Locally Anchored Flow Matching for Coherent Visuomotor Policy

Visuomotor policies aim to learn complex manipulation tasks from expert demonstrations. However, generating smooth and coherent trajectories remains challenging, as it requires balancing proximal precision with distal foresight. Existing approaches typically focus on optimizing intra-chunk action distributions, often neglecting the inter-chunk coherence. Consequently, inter-chunk discontinuities significantly impede the learning of coherent long-horizon actions. To overcome this limitation and achieve a synergetic balance between precision and foresight, we propose FocalPolicy, a foresight-aware visuomotor policy that combines Frequency-Optimized Chunking with Locally Anchored flow matching. We introduce a foresight composite objective that supervises time-domain alignment within the proximal actions while regularizing frequency-domain structure over multiple future action chunks to improve cross-chunk coherence. To efficiently learn complex action distributions, we design locally anchored sampling to enhance target signal propagation efficiency during consistency flow matching training. Extensive experiments demonstrate that FocalPolicy outperforms existing approaches and confirm the generalizability of our modules to other baselines. Project website: https://focalpolicy.github.io/

Qian He, Zhenshuo Yang, Wenqi Liang +3

State Key Laboratory of Robotics and Intelligent Systems, Shenyang Institute of Automation, Chinese Academy of Sciences · University of the Chinese Academy of Sciences · University of Trento

Flow Matching Long-Horizon Robotic Manipulation Visuomotor Policy Learning Robot Imitation Learning Action Chunking

May 15, 2026eess.IV

Flow Matching with Optimized Subclass Priors for Medical Image Augmentation

Rare diseases dominate the diagnostic challenge in medical imaging yet are severely underrepresented in clinical datasets, causing classifiers to fail on exactly the conditions where reliable detection matters most. Generative augmentation can supply the missing tail-class coverage, but coarse disease labels aggregate diverse subtypes and acquisition settings into multi-modal conditionals that bias generators toward dominant submodes, while a shared Gaussian source forces rare subpopulations through disproportionately long transport paths. We propose an offline strategy that introduces informative priors at two levels: first, we partition each coarse label into coherent submodes via Gaussian mixture modeling in the generative model's latent space; second, we learn subclass-conditioned source distributions that re-center and re-scale the starting distribution per submode, shortening trajectories and reducing within-subclass dispersion. To prevent degenerate solutions we impose explicit geometric control, moderately concentrating normalized displacement directions around learnable prototypes while capping path-length outliers. On long-tailed chest X-ray (MIMIC-LT, NIH-LT) and CT slice (CT-RATE) benchmarks the proposed method consistently improves tail-class generation fidelity and diversity (FID, IRS) and is a promising augmentation strategy that reliably improves downstream balanced accuracy and macro-F1 over a non-augmented baseline across modalities.

Felix Nützel, Mischa Dombrowski, Bernhard Kainz

Department of Artificial Intelligence in Biomedical Engineering, Friedrich-Alexander-Universität Erlangen-Nürnberg, 91052 Erlangen, Germany · Department of Computing, Imperial College London, London SW7 2AZ, UK

Flow Matching Synthetic Data Augmentation Long-Tail Learning Medical Image Synthesis Conditional Generative Modeling

May 15, 2026cs.RO

FLASH: Efficient Visuomotor Policy via Sparse Sampling

Generative models such as diffusion and flow matching have become dominant paradigms for visuomotor policy learning, yet their reliance on iterative denoising incurs high inference latency incompatible with real-time robotic control. We present Fast Legendre-polynomial Action policy via Sparse History-anchored flow (FLASH Policy), which replaces discrete action-chunk generation with continuous Legendre polynomial trajectory representation. Specifically, by fitting expert demonstrations under sparse temporal sampling, FLASH enables a single inference to cover a significantly extended action horizon. To further accelerate generation, FLASH initiates the flow matching process from history polynomial coefficients rather than uninformative Gaussian noise, shortening the transport distance and enabling accurate single-step inference. Moreover, analytic polynomial differentiation directly provides desired velocity feed-forward signals to the torque controller without numerical approximation. Extensive experiments on five simulated and two real-world manipulation tasks demonstrate that FLASH achieves state-of-the-art success rates (

\ge 92\%

across all tasks), a per-episode inference time of

31.40\,ms

(up to

175\times

faster than diffusion policies and

18\times

faster than prior flow matching policies), up to

4\times

faster training convergence than ACT, and

5\times

to

7\times

reduction in controller tracking error compared to discrete-action baselines.

Jiaqi Bai, Jindou Jia, Yuxuan Hu +5

MARS Lab, Nanyang Technological University, Singapore

Flow Matching Long-Horizon Robotic Manipulation Robot Skill Learning Visuomotor Policy Learning Policy Learning

May 14, 2026cs.LG

Lagrangian Flow Matching: A Least-Action Framework for Principled Path Design

Flow matching trains a neural velocity field by regression against a target velocity associated with a prescribed probability path connecting a simple initial distribution to the data distribution. A central design choice is the path itself. Existing constructions, including rectified and optimal-transport-based paths, transport samples along straight lines between coupled endpoints and thus cover only a narrow class of dynamics. We observe that this corresponds to the simplest case of the least-action principle in classical mechanics, in which the kinetic Lagrangian yields free-particle straight-line trajectories. Building on this observation, we propose Lagrangian flow matching, a physics-based framework in which the probability path and velocity field are determined by minimizing the action of a general Lagrangian subject to the continuity equation and the prescribed endpoints. We show that this dynamic problem admits an equivalent static optimal transport (OT) formulation, yielding a family of simulation-free training objectives that recover OT-based flow matching as the kinetic special case and the trigonometric variance-preserving diffusion path as the harmonic-oscillator case. More general Lagrangians give rise to new probability paths and velocity fields, and numerical experiments show that they induce meaningful changes in the learned dynamics while remaining competitive with existing conditional flow matching models.

Shukai Du, Junzhe Zhang, Yiming Li

Department of Mathematics, Syracuse University · Department of EECS, Syracuse University

May 14, 2026cs.CV

Aligning Latent Geometry for Spherical Flow Matching in Image Generation

Latent flow matching for image generation usually transports Gaussian noise to variational autoencoder latents along linear paths. Both endpoints, however, concentrate in thin spherical shells, and a Euclidean chord leaves those shells even when preprocessing aligns their radii. By decomposing each latent token into radial and angular components, we show through component-swap probes that decoded perceptual and semantic content is carried predominantly by direction, with radius contributing much less. We therefore project data latents onto a fixed token radius, use the radial projection of Gaussian noise as the spherical prior, finetune the decoder with the encoder frozen, and replace linear interpolation with spherical linear interpolation. The resulting geodesic paths stay on the sphere at every timestep, and their velocity targets are purely angular by construction. Under matched training, the method consistently improves class-conditional ImageNet-256 FID across different image tokenizers, leaves the diffusion architecture unchanged, and requires no auxiliary encoder or representation-alignment objective.

Tuna Han Salih Meral, Kaan Oktay, Hidir Yesiltepe +2

Virginia Tech · fal

Flow Matching Neural Representation Geometry Conditional Image Generation Image Generation Flow-Based Generative Modeling

May 14, 2026cs.CV

EverAnimate: Minute-Scale Human Animation via Latent Flow Restoration

We propose EverAnimate, an efficient post-training method for long-horizon animated video generation that preserves visual quality and character identity. Long-form animation remains challenging because highly dynamic human motion must be synthesized against relatively static environments, making chunk-based generation prone to accumulated drift: (i) low-level quality drift, such as progressive degradation of static backgrounds, and (ii) high-level semantic drift, such as inconsistent character identity and view-dependent attributes. To address this issue, EverAnimate restores drifted flow trajectories by anchoring generation to a persistent latent context memory, consisting of two complementary mechanisms. (i) Persistent Latent Propagation maintains a context memory across chunks to propagate identity and motion in latent space while mitigating temporal forgetting. (ii) Restorative Flow Matching introduces an implicit restoration objective during sampling through velocity adjustment, improving within-chunk fidelity. With only lightweight LoRA tuning, EverAnimate outperforms state-of-the-art long-animation methods in both short- and long-horizon settings: at 10 seconds, it improves PSNR/SSIM by 8%/7% and reduces LPIPS/FID by 22%/11%; at 90 seconds, the gains increase to 15%/15% and 32%/27%, respectively.

Wuyang Li, Yang Gao, Mariam Hassan +4

Flow Matching Long-Horizon Video Generation Memory-Augmented Video Generation Human Motion Generation Flow-Based Generative Modeling Temporal Consistency in Video Generation

May 14, 2026cs.RO

Learning Direct Control Policies with Flow Matching for Autonomous Driving

We present a flow-matching planner for autonomous driving that directly outputs actionable control trajectories defined by acceleration and curvature profiles. The model is conditioned on a bird's-eye-view (BEV) raster of the surrounding scene and generates control sequences in a small number of Ordinary Differential Equations (ODE) integration steps, enabling low-latency inference suitable for real-time closed-loop re-planning. We train exclusively on urban scenarios (real urban city streets, intersections and roundabouts of the city of Parma, Italy) collected from a 2D traffic simulator with reactive agents, and evaluate in closed-loop on both in-distribution and markedly out-of-distribution environments, including multi-lane highways and unseen urban scenarios. Our results show that the model generalizes reliably to these unseen conditions, maintaining stable closed-loop control and successfully completing scenarios that differ substantially from the training distribution. We attribute this to the BEV representation, which provides a geometry-centric view of the scene that is inherently less sensitive to distributional shifts, and to the flow-matching formulation, which learns a smooth vector field that degrades gracefully under distribution shift. We provide video demonstrations of closed-loop behavior at https://marcelloceresini.github.io/DirectControlFlowMatching.

Marcello Ceresini, Federico Pirazzoli, Andrea Bertogalli +5

1Università degli Studi di Parma · 2Alma Mater Studiorum - Università di Bologna · 3VisLab (an Ambarella Inc. company)

Flow Matching End-to-End Autonomous Driving OOD Generalization Autonomous Driving Data-Driven Control Autonomous Driving Planning

May 14, 2026cs.CV

The Velocity Deficit: Initial Energy Injection for Flow Matching

While Flow Matching theoretically guarantees constant-velocity trajectories, we identify a critical breakdown in high-dimensional practice: the Velocity Deficit. We show that the MSE objective systematically underestimates velocity magnitude, causing generated samples to fail to reach the data manifold-a phenomenon we term Integration Lag. To rectify this, we propose Initial Energy Injection, instantiated via two complementary methods: the training-based Magnitude-Aware Flow Matching (MAFM) and the training-free Scale Schedule Corrector (SSC). Both are grounded in our discovery of a crucial asymmetry: velocity contraction causes harmful kinetic stagnation at the trajectory's start, yet acts as a beneficial denoising mechanism at its end. Empirically, SSC yields significant efficiency gains with zero retraining and just one line of code. On ImageNet-1k (256x256), it improves FID by 44.6% (from 13.68 to 7.58) and achieves a 5x speedup, enabling a 50-step generator (FID 7.58) to beat a 250-step baseline (FID 8.65). Furthermore, our methods generalize to Text-to-Image tasks and high-resolution generation, improving FID on MS-COCO by ~22%.

Linze Li, Zong-Wei Hong, Shen Zhang +4

Jiiov Technology, Beijing, China.

Flow Matching Image Generation Flow-Based Generative Modeling Diffusion Model Inference Acceleration

May 14, 2026cs.CV

SpectraFlow: Unifying Structural Pretraining and Frequency Adaptation for Medical Image Segmentation

Medical image segmentation remains challenging in low-data regimes, where scarce annotations often yield poor generalization and ambiguous boundaries with missing fine structures. Recent self-supervised pretraining has improved transferability, but it often exhibits a texture bias. In contrast, accurate segmentation is inherently geometry-aware and depends on both topological consistency and precise boundary preservation. To address this problem, we propose a two-stage framework that couples structure-aware encoder pretraining with boundary-oriented decoding. In Stage-1, we aim to learn structure-aware representations for downstream segmentation in low-data regimes. To this end, we propose Mixed-Domain MeanFlow Pretraining, which aligns images and binary masks in a shared latent space through latent transport regression, where masks act as conditional structural guidance rather than prediction targets, making the pretraining task-agnostic. To further improve training stability under scarce supervision, we incorporate a lightweight Dispersive Loss to prevent representation collapse. In Stage-2, we fine-tune the pretrained encoder with a lightweight decoder that combines Direct Attentional Fusion for adaptive cross-scale gating and Frequency-Directional Dynamic Convolution for high-frequency boundary refinement under appearance variation. Experiments on ISIC-2016, Kvasir-SEG, and GlaS demonstrate consistent gains over state-of-the-art methods, with improved robustness in low-data settings and sharper boundary delineation.

Zhiquan Chen, Haitao Wang, Guowei Zou +1

School of Computer Science and Engineering, Sun Yat-sen University, Guangzhou, China · Guangdong Key Laboratory of Big Data Analysis and Processing, Guangzhou, China

Flow Matching Image Segmentation Self-Supervised Pre-Training Medical Image Segmentation Boundary-Aware Segmentation Medical Image Representation Learning+1

May 13, 2026cs.LG

WarmPrior: Straightening Flow-Matching Policies with Temporal Priors

Generative policies based on diffusion and flow matching have become a dominant paradigm for visuomotor robotic control. We show that replacing the standard Gaussian source distribution with WarmPrior, a simple temporally grounded prior constructed from readily available recent action history, consistently improves success rates on robotic manipulation tasks. We trace this gain to markedly straighter probability paths, echoing the effect of optimal-transport couplings in Rectified Flow. Beyond standard behavior cloning, WarmPrior also reshapes the exploration distribution in prior-space reinforcement learning, improving both sample efficiency and final performance. Collectively, these results identify the source distribution as an important and underexplored design axis in generative robot control.

Sinjae Kang, Chanyoung Kim, Kaixin Wang +2

KAIST · Microsoft Research

Flow Matching Visuomotor Policy Learning Diffusion Policy Robotic Manipulation RL for Generative Models

May 13, 2026cs.LG

Sampling from Flow Language Models via Marginal-Conditioned Bridges

Flow Language Models (FLMs) are a recently introduced class of language models which adapt continuous flow matching for one-hot encoded token sequences. Their denoisers have a special structure absent from generic continuous diffusion models: each block of the denoising mean is a posterior marginal distribution over the clean token at that position. Standard DDPM-style samplers collapse these marginals to a single conditional-mean endpoint and bridge toward this simplex-valued point, which is generally not a valid one-hot sequence. We argue that the natural sampler for an FLM is instead posterior-predictive. At each reverse step, we sample a clean one-hot endpoint from the factorized posterior defined by the FLM token marginals, and then sample the next continuous state from the analytic Ornstein--Uhlenbeck bridge conditioned on that endpoint. The method is training-free, uses the same model evaluations as standard sampling, and gives a principled interface for token-level decoding controls such as temperature scaling and nucleus truncation. We show that, under exact posterior marginals, the endpoint approximation error is exactly the conditional multi-information among token positions. The induced one-step bridge kernel preserves all token-wise posterior-predictive marginals and loses only the residual cross-position dependence. Finally, we prove a Girsanov path-space comparison showing that the marginal-conditioned bridge has a no-larger denoising-error term than the frozen conditional-mean bridge, with strict improvement whenever intermediate coordinate-wise bridge observations reveal additional information about the clean token. Experiments with FLMs show that the sampler improves the quality--diversity tradeoff. Code is available at: github.com/imbirik/mcb.

Iskander Azangulov, Leo Zhang

Department of Statistics, University of Oxford

Flow Matching Language Model Decoding Language Modeling Flow-Based Generative Modeling

May 13, 2026cs.LG

Path-independent Flow Matching for Multi-parameter Generative Dynamics

Flow Matching is a powerful framework for learning transport maps between probability distributions. Yet its standard single-parameter formulation is not designed to capture multi-parameter variations where the resulting transport should be path-independent. Path independence is crucial because it ensures that transformations depend only on the initial and target distributions, not on the specific path. In this work, we introduce Path-independent Flow Matching (PiFM), a method for learning vector fields whose induced flows yield path-independent transport between distributions. We show that PiFM generalizes Flow Matching to higher-dimensional parameter domains while enforcing structural conditions that ensure consistency of composed transformations. In addition, we show that, under suitable assumptions, PiFM approximates the Wasserstein barycenter, linking the framework to a notion of distributional interpolation. To enable practical training, we propose a tractable, simulation-free objective that regresses onto multi-parameter conditional probability paths. We showcase empirically that PiFM outperforms other approaches on both synthetic and real world data in interpolating path-independent trajectories and generating desired out of distribution samples.

Francisco Téllez, AmirHossein Zamani, Philippe Martin +5

Université de Montréal, Mila · Concordia University, Mila · Concordia University +2

Flow Matching Flow Map Learning Generative Modeling Flow-Based Generative Modeling Optimal Transport

May 13, 2026cs.LG

Support-Conditioned Flow Matching Is Kernel Smoothing

Generative models are often conditioned on a small set of examples via cross-attention. Under the Gaussian optimal-transport path, we show that the exact velocity field induced by a finite support set is a Nadaraya--Watson kernel smoother whose bandwidth decreases with flow time, from broad averaging at early steps to nearest-neighbor at late steps. A single Gaussian-kernel attention head exactly computes this field, connecting cross-attention conditioning to classical kernel theory. The theory predicts three failure regimes: nearest-neighbor collapse of the kernel at high dimension, mismatch between the isotropic kernel and the data geometry, and insufficient support for nonparametric estimation. Experiments on Gaussian mixtures, spherical shells, and DINOv2 ImageNet features confirm that learned conditioning improves in precisely these regimes, and that IP-Adapter's cross-attention implements approximate NW smoothing in practice.

Daniel Matsui Smola

Department of Computer Science University of Washington Seattle, WA

Flow Matching Cross-Attention Kernel Methods Flow-Based Generative Modeling Conditional Generative Modeling