Flow Matching

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Overview

Flow matching learns a velocity field that moves samples from a simple source, often Gaussian noise, toward a target data distribution. Conditional flow matching trains the field on paths between source and data samples, while optimal-transport couplings and rectified paths aim to make those trajectories easier to learn and integrate with an ordinary differential equation solver. Extensions handle discrete data, curved manifolds and symmetries, physical constraints, and applications from image and speech generation to robotics, scientific forecasting, and inverse problems. A central challenge is getting high fidelity and diverse, reliable samples with few solver steps; theory on convergence and stability is advancing, but the best paths, source distributions, and schedules depend on the task.

Latest papers

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663 papers123 papers in the last four weeks, up 68% on the four weeks before. 0.7% of all new papers.

May 1, 2026

Flow matching for Sentinel-2 super-resolution: implementation, application, and implications

Developing robust techniques for super-resolution of satellite imagery involves navigating commonly observed trade-offs between spectral fidelity and perceptual quality. In this work, we introduce a flow matching model for 4x super-resolution of 10-m Sentinel-2 visible and near-infrared bands over the conterminous United States (CONUS) using a dataset of 120,851 10-m Sentinel-2 and 2.5-m resampled NAIP imagery pairs acquired on the same day. Our results showed that the flow matching model outperformed diffusion and Real-ESRGAN models in pixel-wise accuracy in a single sampling step using the Euler method. When evaluated with a second-order Midpoint solver, our model generated perceptually realistic super-resolved imagery in only 20 sampling steps, effectively navigating the perception-distortion trade-off at inference time without retraining. We used this model to produce a super-resolved 2.5-m 4-band CONUS imagery product derived from 2025 10-m Sentinel-2 annual composites, consisting of over 1.58 trillion pixels. We further evaluated the use of super-resolved data on a land cover classification task using semantic segmentation models. Finally, we generated a yearly 2.5-m land cover product for the Chesapeake Bay watershed for 2020-2025. An accuracy assessment against 25,000 ground truth points revealed an overall accuracy of 89.11% for the annual land cover product. We conclude that flow matching is an effective generative modeling approach for super-resolution of Sentinel-2 imagery compared to diffusion and Generative Adversarial Network-based methods, and has strong implications for expanding access to high-resolution imagery for geospatial applications that demand fine spatial detail.

Dakota Hester, Vitor S. Martins, Lucas B. Ferreira +2

Department of Agricultural and Biological Engineering, Mississippi State University · North Mississippi Research and Extension Center, Mississippi State University

Flow MatchingLand Cover ClassificationRemote Sensing Image Super-ResolutionRemote SensingImage Super-Resolution
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May 1, 2026

Binomial flows: Denoising and flow matching for discrete ordinal data

Flow-based generative modeling in continuous spaces exploit Tweedie's formula to express the denoiser (learned in training) as a score function (used in sampling). In contrast, this relation has been largely missing in the discrete setting where common approaches focus on learning discrete scores and rates. In this work we close this gap for discrete non-negative ordinal data by introducing Binomial flows. Our framework provides a simple recipe for training a discrete diffusion model which simultaneously denoises, samples, and estimates exact likelihoods. We verify our methodology on synthetic examples and obtain competitive results on real-world data sets.

Yair Shenfeld, Ricardo Baptista, Stefano Peluchetti

Flow MatchingFlow-Based Generative ModelingDiffusion ModelsDiscrete Flow Matching
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May 1, 2026

Free Energy Surface Sampling via Reduced Flow Matching

Sampling the free energy surface, namely, the distribution of collective variables (CVs), is a crucial problem in statistical physics, as it underpins a better understanding of chemical reactions and conformational transitions. Traditional methods for free energy surface sampling involve simulation in high-dimensional configuration space and projecting the resulting configurations onto the CV space. To reduce the computational costs of such sampling, we propose FES-FM, a reduced flow matching (FM) method for free energy sampling (FES). We train a dynamical transport map in the CV space, thereby enabling direct sampling of the free energy surface. For many-particle systems, we construct a prior distribution based on the Hessian at a local minimum of the potential, which ensures both rotation-translation invariance and physically meaningful configurations. We evaluate the proposed method across a variety of potential functions and collective variables. Comparative experiments demonstrate that our approach drastically reduces computational costs while delivering superior accuracy per unit sampling time.

Zichen Liu, Tiejun Li

Center for Data Science, Peking University · LMAM and School of Mathematical Sciences, Peking University · Center for Machine Learning Research, Peking University

Free Energy CalculationFlow MatchingMolecular Dynamics Simulation
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Apr 30, 2026

StyleShield: Exposing the Fragility of AIGC Detectors through Continuous Controllable Style Transfer

AI-generated content (AIGC) detectors are increasingly deployed in high-stakes settings such as academic integrity screening, yet their reliability rests on a fundamental paradox: as language models are trained on human-written corpora, the statistical boundary between AI and human writing will inevitably dissolve as models improve. Commercial incentives have further distorted this landscape -- detection services and "de-AIification" tools often operate within the same supply chain, replacing evaluation of content quality with judgment of content origin. We present StyleShield, the first flow matching framework for conditional text style transfer, operating directly in continuous token embedding space via a DiT backbone with zero-initialized cross-attention adapters conditioned on frozen Qwen-7B representations. At inference, we adapt the SDEdit paradigm from image synthesis to text embeddings, with a single parameter gamma providing smooth continuous control over the evasion-preservation trade-off. On a multi-domain Chinese benchmark, StyleShield achieves 94.6% evasion against the training detector and >=99% against three unseen detectors, maintaining 0.928 semantic similarity. We further introduce RateAudit, a document-level scheduling algorithm that demonstrates detection-rate verdicts can be set to arbitrary values, directly questioning the reliability of score-based evaluation.

Guantian Zheng

Flow MatchingAI-Generated Text DetectionText Style TransferRobustness of Machine-Generated Text DetectionText GenerationAdversarial Text Attacks
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Apr 28, 2026

FlowS: One-Step Motion Prediction via Local Transport Conditioning

Generative motion prediction must satisfy three simultaneous requirements for real-world autonomy: high accuracy, diverse multimodal futures, and strictly bounded latency. Diffusion models meet the first two but violate the third, requiring tens to hundreds of denoising steps. We identify a conditioning strategy that resolves this tension: single-step integration is accurate when the underlying transport problem is local. A model that must both discover the correct behavioral mode and traverse a long displacement in one step accumulates large discretization errors; conditioning the base distribution to lie near plausible futures reduces the problem to short-range refinement, the regime where a single Euler step suffices. We instantiate this local transport conditioning in FlowS, a conditional flow matching framework with two mechanisms. First, an online, scene-conditioned learned prior emits KK calibrated anchor trajectories per agent, each already near a plausible future, converting mode discovery into local correction. Second, a step-consistent displacement field enforces semigroup self-consistency, guaranteeing that a single step inherits multi-step accuracy. Crucially, anchoring this field at learned priors along straight-line paths yields a {stable, low-variance} training target, unlike prior self-consistency methods that suffer from {high-variance bootstrap} signals on curved diffusion paths. On the Waymo Open Motion Dataset, FlowS achieves state-of-the-art Soft mAP {(0.4804) and mAP (0.4703) with ensemble at 75,FPS} with single-step inference, demonstrating that local transport conditioning makes one-step generative motion prediction practical for safety-critical autonomy. Code and pretrained models will be released upon acceptance.

Leandro Di Bella, Adrian Munteanu, Bruno Cornelis

Department of Electronics and Informatics, Vrije Universiteit Brussel, Pleinlaan 2, B-1050 Brussels, Belgium. · IMEC, Kapeldreef 75, B-3001 Leuven, Belgium.

Flow MatchingTrajectory GenerationMulti-Agent Trajectory PredictionAutonomous Driving PerceptionOne-Step Generative ModelingFlow-Based Generative Modeling+2
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Apr 28, 2026

PhyloSDF: Phylogenetically-Conditioned Neural Generation of 3D Skull Morphology via Residual Flow Matching

Generating novel, biologically plausible three-dimensional morphological structures is a fundamental challenge in computational evolutionary biology, hampered by extreme data scarcity and the requirement that generated shapes respect phylogenetic relationships among species. In this work, we present PhyloSDF, a phylogenetically-conditioned neural generative model for 3D biological morphology that integrates two innovations: (1) a DeepSDF auto-decoder regularized by a novel Phylogenetic Consistency Loss that structures the latent space to correlate with evolutionary distances (Pearson r=0.993); (2) a Residual Conditional Flow Matching (Residual CFM) architecture that factorizes generation into analytic species-centroid lookup and learned residual prediction, enabling generation from as few as ~4 specimens per species. We evaluate PhyloSDF on 100 micro-CT-scanned skulls of Darwin's Finches and their relatives across 24 species. The model generates novel meshes achieving 88-129% of real intra-species variation at the code level, with all 180 generated meshes verified as non-memorized. Residual CFM surpasses denoising diffusion (which fails entirely at this scale), standard flow matching (which mode-collapses to 3-6% variation), and a Gaussian mixture baseline in both fidelity (Chamfer Distance 0.00181 vs. 0.00190) and morphometric Fréchet distance (10,641 vs. 13,322). Leave-one-species-out experiments across 18 species demonstrate phylogenetic extrapolation capability, and smooth latent interpolations produce biologically plausible ancestral skull reconstructions.

Kaikwan Lau, Gary P. T. Choi

Department of Mathematics The Chinese University of Hong Kong

Flow Matching3D Mesh Generation3D Shape GenerationConditional Generative Modeling
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Apr 27, 2026

Learning biophysical models of gene regulation with probability flow matching

Cellular differentiation is governed by gene regulatory networks, the high-dimensional stochastic biochemical systems that determine the transcriptional landscape and mediate cellular responses to signals and perturbations. Although single-cell RNA sequencing provides quantitative snapshots of the transcriptome, current methods for inferring gene-regulatory dynamics often lack mechanistic interpretability and fail to generalize to unseen conditions. Here we introduce Probability Flow Matching (PFM), a scalable framework for learning biophysically consistent stochastic processes directly from time-resolved single-cell measurements. Applying PFM to three hematopoiesis datasets, we show that models with similar interpolation accuracy can encode fundamentally different dynamics, with only biophysically consistent formulations accurately capturing mechanisms of lineage transitions, fate specification, and gene perturbation responses. We further demonstrate that PFM accommodates unbalanced populations, enabling simultaneous inference of cellular proliferation and death dynamics. Together, these results establish PFM as a flexible, scalable framework for integrating mechanistic modeling with single-cell omics.

Suryanarayana Maddu, Victor Chardès, Michael J. Shelley

Center for Computational Biology, Flatiron Institute, New York, NY, USA, 10010 · Molecular & Cellular Biology Department, Harvard University, Cambridge, MA 02138 · Courant Institute of Mathematical Sciences, New York University, New York, NY, USA, 10012

Flow MatchingSingle-Cell Perturbation ModelingGene Regulatory Network InferenceSingle-Cell Transcriptomics
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Apr 27, 2026

Point-MF: One-step Point Cloud Generation from a Single Image via Mean Flows

Single-image point cloud reconstruction must infer complete 3D geometry, including occluded parts, from a single RGB image. While diffusion-based reconstructors achieve high accuracy, they typically require many denoising iterations, resulting in slow and expensive inference. We propose Point-MF, a Mean-Flow-based framework for low-NFE single-image point cloud reconstruction that couples a Mean-Flow-compatible architecture with an auxiliary loss. Specifically, Point-MF operates directly in point-cloud space to learn the mean velocity field and enables one-step reconstruction with a single network function evaluation (1-NFE), without relying on VAE-based latent representations. To make Mean Flow effective under large interval jumps, Point-MF employs a Diffusion Transformer tailored to the Mean-Flow setting, conditioned on frozen DINOv3 image features via a lightweight token adapter and equipped with explicit interval/time conditioning. Moreover, we introduce Denoised Space Anchor, a set-distance auxiliary loss on the denoised-space estimate xθx_θ induced by the predicted velocity field, to stabilize large-step generation and reduce outliers and density artifacts. On ShapeNet-R2N2 and Pix3D, Point-MF strikes a strong balance between reconstruction quality and inference speed compared to multi-step diffusion baselines and competitive feedforward models, while generating high-quality point clouds with millisecond-level latency.

Yuta Baba, Keiji Yanai

The University of Electro-Communications 1-5-1 Chofugaoka, Chofu-shi, Tokyo 182-8585, Japan

Flow MatchingOne-Step Generative ModelingMean FlowPoint Cloud GenerationSingle-View 3D Reconstruction
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Apr 26, 2026

FlowPlace: Flow Matching for Chip Placement

Chip placement plays an important role in physical design. While generative models like diffusion models offer promising learning-based solutions, current methods have the following limitations: they use random synthetic data for pre-training, require long sampling times, and often result in overlaps due to their dependence on gradient-based solvers during the sampling process. To overcome these issues, we propose FlowPlace, which features mask-guided synthetic data generation, flow-based efficient training with flexible prior injection, and hard constraint sampling for overlap-free layouts. Experiments on OpenROAD and ICCAD 2015 benchmarks show FlowPlace achieves better PPA metrics, 10-50×\times faster sampling efficiency, and zero overlaps.

Peng Xie, Ke Xue, Yunqi Shi +6

1State Key Laboratory of Novel Software Technology, Nanjing University, China · School of Artificial Intelligence, Nanjing University, China · 3Huawei Noah’s Ark Lab, China

Constrained Generative ModelingFlow MatchingElectronic Design AutomationGenerative ModelingFlow-Based Generative Modeling
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Apr 26, 2026

Adversarial Flow Matching for Imperceptible Attacks on End-to-End Autonomous Driving

Autonomous driving (AD) is evolving towards end-to-end (E2E) frameworks through two primary paradigms: monolithic models exemplified by Vision-Language-Action (VLA), and specialized modular architectures. Despite their divergent designs, both paradigms increasingly rely on Transformer backbones for complex reasoning, potentially causing a shared vulnerability: visually imperceptible perturbations can manipulate E2E AD models into hazardous maneuvers by targeting the Transformer module. Most existing adversarial attack approaches against AD systems operate under white-box or black-box settings; yet, they typically necessitate full model transparency, or suffer from either prohibitive query latency or limited attack transferability. In this paper, we propose Adversarial Flow Matching (AFM), a novel gray-box attack framework that exploits Transformer structural vulnerabilities in E2E AD models. AFM enables efficient one-step generation of adversarial examples via a neural average velocity field. Additionally, the proposed technique yields effective and visually imperceptible attacks by synergistically perturbing the generative latent space and the neural average velocity field. Extensive experiments demonstrate that AFM achieves a superior trade-off between attack effectiveness and imperceptibility: it substantially degrades the performance of both VLA and modular AD agents across various scenarios compared to baselines, while maintaining state-of-the-art visual imperceptibility. Furthermore, adversarial examples generated by AFM exhibit robust cross-model transferability, indicating that AFM closely approximates a black-box attack setting while requiring only the prior knowledge that the target AD model incorporates a Transformer-based module.

Xinyu Zeng, Xiangkun He, Lei Tao +2

Shenzhen Institute for Advanced Study, University of Electronic Science and Technology of China, Shenzhen 518110, China · School of Mechanical and Aerospace Engineering, Nanyang Technological University, Singapore 639798 · School of Mechanical and Electrical Engineering, University of Electronic Science and Technology of China, Chengdu 611731, China

Flow MatchingEnd-to-End Autonomous DrivingAdversarial AttacksAdversarial Transferability
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Apr 25, 2026

MotionHiFlow: Text-to-motion via hierarchical flow matching

Text-to-motion generation aims to generate 3D human motions that are tightly aligned with the input text while remaining physically plausible and rich in fine-grained detail. Although recent approaches can produce complex and natural movements, they usually operate at only one temporal scale, which limits both semantic alignment and temporal coherence. Inspired by the fact that complex motions are conceptualized hierarchically rather than at a single temporal scale in the human cognitive system, we propose MotionHiFlow, a hierarchical flow matching framework to generate motion progressively by constructing flow path from low to high temporal scales. The flows at lower scales capture high-level semantics and coarse motion structures, while flows at higher scales refine temporal details. To link the flows across scales, we introduce a novel cross-scale transition process, ensuring continuity and preserving noise consistency. Furthermore, by integrating a Text-Motion Diffusion Transformer and a topology-aware Motion VAE, MotionHiFlow explicitly models structural dependencies among joints via joint-aware positional encoding and skeletal topology, enabling precise semantic alignment alongside fine-grained motion details. Extensive experiments on HumanML3D and KIT-ML benchmarks demonstrate state-of-the-art performance, with ablation studies confirming the effectiveness of the hierarchical design and key components. Code is available at https://github.com/ai-lh/MotionHiFlow.

Heng Li, Xiaotong Lin, Ling-An Zeng +3

Sun Yat-sen University · Shandong University · Guangdong Province Key Laboratory of Information Security Technology, China +1

Flow MatchingText-to-Motion GenerationHuman Motion GenerationFlow-Based Generative Modeling
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Apr 23, 2026

Null-Space Flow Matching for MIMO Channel Estimation in Latency-Constrained Systems

Accurate yet low-latency channel state information (CSI) acquisition is essential for multiple-input multiple-output (MIMO) communication systems. While advanced deep generative models, such as score-based and diffusion models, enable high-fidelity CSI reconstruction from limited pilot observations, they often suffer from high inference latency. To achieve accurate CSI estimation under stringent latency constraints, this paper proposes a null-space flow matching (FM) framework that decomposes pilot-limited MIMO channel estimation into a range-space reconstruction problem and a null-space generation problem. Specifically, the range-space component of the channel is directly recovered from noisy pilot observations, while only the ambiguous null-space component is iteratively refined using an FM-based generative prior. To further improve the robustness of the proposed framework, we introduce a power-law time schedule to better allocate the limited number of refinement steps, along with a noise-aware adaptive correction strategy to suppress channel noise on the refinement trajectory. Experimental results demonstrate that our method achieves a competitive normalized mean square error (NMSE) even under a strict latency budget of around 3 ms, while delivering superior estimation accuracy and faster inference than both model-based and generative baselines.

Junjie Zhao, Guangming Liang, Dongzhu Liu +1

College of Electronic Information and Optical Engineering, Nankai University · School of Computing Science, University of Glasgow · School of Natural and Computing Science, University of Aberdeen

Flow MatchingEfficient InferenceWireless CommunicationsChannel Estimation
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Apr 22, 2026

WFM: 3D Wavelet Flow Matching for Ultrafast Multi-Modal MRI Synthesis

Diffusion models have achieved remarkable quality in multi-modal MRI synthesis, but their computational cost (hundreds of sampling steps and separate models per modality) limits clinical deployment. We observe that this inefficiency stems from an unnecessary starting point: diffusion begins from pure noise, discarding the structural information already present in available MRI sequences. We propose WFM (Wavelet Flow Matching), which instead learns a direct flow from an informed prior, the mean of conditioning modalities in wavelet space, to the target distribution. Because the source and target share underlying anatomy and differ primarily in contrast, this formulation enables accurate synthesis in just 1-2 integration steps. A single 82M-parameter model with class conditioning synthesizes all four BraTS modalities (T1, T1c, T2, FLAIR), replacing four separate diffusion models totaling 326M parameters. On BraTS 2024, WFM achieves 26.8 dB PSNR and 0.94 SSIM, within 1-2 dB of diffusion baselines, while running 250-1000x faster (0.16-0.64s vs. 160s per volume). This speed-quality trade-off makes real-time MRI synthesis practical for clinical workflows. Code is available at https://github.com/yalcintur/WFM.

Yalcin Tur, Mihajlo Stojkovic, Ulas Bagci

Department of Computer Science, Stanford University, Stanford, CA, USA · Machine and Hybrid Intelligence Lab, Feinberg School of Medicine, Northwestern University, Chicago, IL, USA

Flow MatchingBraTSMagnetic Resonance ImagingMedical Image Synthesis
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Apr 22, 2026

On the Role of Strain and Vorticity in Numerical Integration Error for Flow Matching

Flow matching generates data by integrating a learned velocity field, where the number of integration steps (NFE) directly determines inference cost. We analyze which properties of the velocity field govern integration error by decomposing the velocity Jacobian into its symmetric part S (strain rate) and antisymmetric part Omega (vorticity). We prove that strain and vorticity play different roles: strain controls exponential error amplification through the logarithmic norm, while vorticity contributes only linearly to the local truncation error. We further show that the optimal transport velocity field is irrotational and has zero material derivative, implying second-order Euler accuracy; for exact displacement interpolation, the associated Lagrangian particle dynamics are integrated exactly by Euler. Motivated by this analysis, we study weighted Jacobian regularization with strain weight alpha and vorticity weight beta. Experiments on 2D synthetic data confirm the main theoretical predictions, showing up to 2.7x lower integration error at NFE=5. Preliminary CIFAR-10 experiments show consistent trends, with a lightweight fine-tuning procedure improving FID by 14 percent at NFE=10 while preserving high-NFE quality.

Chenxi Tao, Seung-Kyum Choi

Georgia Institute of Technology

Flow MatchingJacobian RegularizationNumerical Integration
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Apr 22, 2026

Tokenised Flow Matching for Hierarchical Simulation Based Inference

The cost of simulator evaluations is a key practical bottleneck for Simulation Based Inference (SBI). In hierarchical settings with shared global parameters and exchangeable site-level parameters and observations, this structure can be exploited to improve simulation efficiency. Existing hierarchical SBI approaches factorise the posterior yet still simulate across multiple sites per training sample; We instead explore likelihood factorisation (LF) to train from single-site simulations. In LF sampling we learn a per-site neural surrogate of the simulator and then assemble synthetic multi-site observations to amortise inference for the full hierarchical posterior. Building on this, we propose Tokenised Flow Matching for Posterior Estimation (TFMPE), a tokenised flow matching approach that supports function-valued observations through likelihood factorisation. To enable systematic evaluation, we introduce a benchmark for hierarchical SBI. We validate TFMPE on this benchmark and on realistic infectious disease and computational fluid dynamics models, finding well-calibrated posteriors while reducing computational cost.

Giovanni Charles, Cosmo Santoni, Seth Flaxman +1

Imperial College London, London, United Kingdom · University of Oxford, Oxford, United Kingdom

Flow MatchingSimulation-Based InferenceBayesian InferenceHierarchical Bayesian Modeling
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Apr 22, 2026

Stability-Driven Motion Generation for Object-Guided Human-Human Co-Manipulation

Co-manipulation requires multiple humans to synchronize their motions with a shared object while ensuring reasonable interactions, maintaining natural poses, and preserving stable states. However, most existing motion generation approaches are designed for single-character scenarios or fail to account for payload-induced dynamics. In this work, we propose a flow-matching framework that ensures the generated co-manipulation motions align with the intended goals while maintaining naturalness and effectiveness. Specifically, we first introduce a generative model that derives explicit manipulation strategies from the object's affordance and spatial configuration, which guide the motion flow toward successful manipulation. To improve motion quality, we then design an adversarial interaction prior that promotes natural individual poses and realistic inter-person interactions during co-manipulation. In addition, we also incorporate a stability-driven simulation into the flow matching process, which refines unstable interaction states through sampling-based optimization and directly adjusts the vector field regression to promote more effective manipulation. The experimental results demonstrate that our method achieves higher contact accuracy, lower penetration, and better distributional fidelity compared to state-of-the-art human-object interaction baselines. The code is available at https://github.com/boycehbz/StaCOM.

Jiahao Xu, Xiaohan Yuan, Xingchen Wu +3

1Tianjin University · 2National University of Singapore · 3Sichuan University

HOI GenerationFlow MatchingHuman Motion GenerationHuman-Object Interaction
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Apr 22, 2026

Semi-Supervised Flow Matching for Mosaiced and Panchromatic Fusion Imaging

Fusing a low resolution (LR) mosaiced hyperspectral image (HSI) with a high resolution (HR) panchromatic (PAN) image offers a promising avenue for video-rate HR-HSI imaging via single-shot acquisition, yet its severely ill-posed nature remains a significant challenge. In this work, we propose a novel semi-supervised flow matching framework for mosaiced and PAN image fusion. Unlike previous diffusion-based approaches constrained by specific protocols or handcrafted assumptions, our method seamlessly integrates an unsupervised scheme with flow matching, resulting in a generalizable and efficient generative framework. Specifically, our method follows a two-stage training pipeline. First, we pretrain an unsupervised prior network to produce an initial pseudo HR-HSI. Building on this, we then train a conditional flow matching model to generate the target HR-HSI, introducing a random voting mechanism that iteratively refines the initial HR-HSI estimate, enabling robust and effective fusion. During inference, we employ a conflict-free gradient guidance strategy that ensures spectrally and spatially consistent HR-HSI reconstruction. Experiments on multiple benchmark datasets demonstrate that our method achieves superior quantitative and qualitative performance by a significant margin compared to representative baselines. Beyond mosaiced and PAN fusion, our approach provides a flexible generative framework that can be readily extended to other image fusion tasks and integrated with unsupervised or blind image restoration algorithms.

Peiming Luo, Nan Wang, Litong Liu +4

Southeast University · Hunan University

Flow MatchingMulti-Source Image FusionHyperspectral ImagingMultimodal Fusion
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Apr 21, 2026

Frequency-Forcing: From Scaling-as-Time to Soft Frequency Guidance

While standard flow-matching models transport noise to data uniformly, incorporating an explicit generation order - specifically, establishing coarse, low-frequency structure before fine detail - has proven highly effective for synthesizing natural images. Two recent works offer distinct paradigms for this. K-Flow imposes a hard frequency constraint by reinterpreting a frequency scaling variable as flow time, running the trajectory inside a transformed amplitude space. Latent Forcing provides a soft ordering mechanism by coupling the pixel flow with an auxiliary semantic latent flow via asynchronous time schedules, leaving the pixel interpolation path itself untouched. Viewed from the angle of improving pixel generation, we observe that forcing - guiding generation with an earlier-maturing auxiliary stream - offers a highly compatible route to scale-ordered generation without rewriting the core flow coordinate. Building on this, we propose Frequency-Forcing, which realizes K-Flow's frequency ordering through Latent Forcing's soft mechanism: a standard pixel flow is guided by an auxiliary low-frequency stream that matures earlier in time. Unlike Latent Forcing, whose scratchpad relies on a heavy pretrained encoder (e.g., DINO), our frequency scratchpad is derived from the data itself via a lightweight learnable wavelet packet transform. We term this a self-forcing signal, which avoids external dependencies while learning a basis better adapted to data statistics than the fixed bases used in hard frequency flows. On ImageNet-256, Frequency-Forcing consistently improves FID over strong pixel- and latent-space baselines, and naturally composes with a semantic stream to yield further gains. This illustrates that forcing-based scale ordering is a versatile, path-preserving alternative to hard frequency flows.

Weitao Du

DAMO Academy

Flow MatchingImage GenerationFlow-Based Generative Modeling
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Apr 21, 2026

MedFlowSeg: Flow Matching for Medical Image Segmentation with Frequency-Aware Attention

Flow matching has recently emerged as a principled framework for learning continuous-time transport maps, enabling efficient ODE-based sampling without relying on stochastic diffusion processes. While generative modeling has shown promise for medical image segmentation, particularly in capturing uncertainty and complex anatomical variability, existing approaches are predominantly based on diffusion models, which require iterative sampling and incur substantial computational overhead. In this work, we propose MedFlowSeg, a conditional flow matching framework that formulates medical image segmentation as learning a time-dependent vector field that transports a simple prior distribution to the target segmentation distribution. Compared to diffusion-based methods, our formulation enables more efficient inference through solving an ordinary differential equation, while preserving the flexibility of generative modeling. To effectively incorporate conditional information, we introduce a dual-conditioning mechanism. Specifically, we propose a Dual-Branch Spatial Attention (DB-SA) module to inject multi-frequency structural priors, and a Frequency-Aware Attention (FA-Attention) module to model interactions between spatial and spectral representations via discrepancy-aware fusion and time-dependent modulation. These components improve the alignment between noisy intermediate states and clean semantic features, leading to better structural consistency and boundary delineation. We conduct extensive experiments across multiple medical imaging modalities, where MedFlowSeg consistently outperforms prior state-of-the-art (SOTA) baselines, including diffusion-based and flow-based methods.

Zhi Chen, Runze Hu, Le Zhang

School of Engineering, University of Birmingham · School of Public Health, Peking University

Flow MatchingMedical Image Segmentation
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Apr 21, 2026

Allo{SR}2^2: Rectifying One-Step Super-Resolution to Stay Real via Allomorphic Generative Flows

Real-world image super-resolution (Real-SR) has been revolutionized by leveraging the powerful generative priors from Diffusion Models (DMs) and Flow Matching (FM). However, existing one-step methods typically replace Gaussian noise with degraded low-resolution (LR) latents at initialization, introducing a substantial distribution shift that further leads to trajectory deviation and prior collapse under extreme acceleration. To overcome these limitations, we propose Allo{SR}2^2, a novel FM-based framework that rectifies one-step SR flows via allomorphic generative flows to maintain high-fidelity generative realism. Specifically, we utilize SNR-Guided Trajectory Initialization to identify a statistically aligned intermediate state along the pre-trained path to integrate LR representations into the generative flow. To ensure a stable, low-curvature path for one-step inference, we propose Flow-Anchored Trajectory Consistency (FATC), which explicitly regularizes the velocity field of the underlying probability flow. Furthermore, we develop Allomorphic Trajectory Matching (ATM), a self-adversarial distillation strategy that jointly models the SR flow and the generative flow within a unified velocity field, enabling one-step Real-SR while preserving the generative prior. Extensive experiments on both synthetic and real-world benchmarks demonstrate that Allo{SR}2^2 achieves state-of-the-art performance in one-step Real-SR, offering a superior balance between fidelity and realism while maintaining extreme efficiency.

Zihan Wang, Xudong Huang, Junbo Qiao +4

East China Normal University · Huawei Foundation Model Dept. · Key Laboratory of Advanced Theory and Application in Statistics and Data Science

Flow MatchingDiffusion Model DistillationOne-Step Generative ModelingImage Super-Resolution
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Apr 20, 2026

Extending One-Step Image Generation from Class Labels to Text via Discriminative Text Representation

Few-step generation has been a long-standing goal, with recent one-step generation methods exemplified by MeanFlow achieving remarkable results. Existing research on MeanFlow primarily focuses on class-to-image generation. However, an intuitive yet unexplored direction is to extend the condition from fixed class labels to flexible text inputs, enabling richer content creation. Compared to the limited class labels, text conditions pose greater challenges to the model's understanding capability, necessitating the effective integration of powerful text encoders into the MeanFlow framework. Surprisingly, although incorporating text conditions appears straightforward, we find that integrating powerful LLM-based text encoders using conventional training strategies results in unsatisfactory performance. To uncover the underlying cause, we conduct detailed analyses and reveal that, due to the extremely limited number of refinement steps in the MeanFlow generation, such as only one step, the text feature representations are required to possess sufficiently high discriminability. This also explains why discrete and easily distinguishable class features perform well within the MeanFlow framework. Guided by these insights, we leverage a powerful LLM-based text encoder validated to possess the required semantic properties and adapt the MeanFlow generation process to this framework, resulting in efficient text-conditioned synthesis for the first time. Furthermore, we validate our approach on the widely used diffusion model, demonstrating significant generation performance improvements. We hope this work provides a general and practical reference for future research on text-conditioned MeanFlow generation. The code is available at https://github.com/AMAP-ML/EMF.

Chenxi Zhao, Chen Zhu, Xiaokun Feng +6

College of Computer Science, Nankai University · AMAP, Alibaba Group

Flow MatchingRepresentation LearningConditional Image GenerationT2I GenerationOne-Step Generative Modeling
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Apr 20, 2026

Fisher Decorator: Refining Flow Policy via a Local Transport Map

Recent advances in flow-based offline reinforcement learning (RL) have achieved strong performance by parameterizing policies via flow matching. However, they still face critical trade-offs among expressiveness, optimality, and efficiency. In particular, existing flow policies interpret the L2L_2 regularization as an upper bound of the 2-Wasserstein distance (W2W_2), which can be problematic in offline settings. This issue stems from a fundamental geometric mismatch: the behavioral policy manifold is inherently anisotropic, whereas the L2L_2 (or upper bound of W2W_2) regularization is isotropic and density-insensitive, leading to systematically misaligned optimization directions. To address this, we revisit offline RL from a geometric perspective and show that policy refinement can be formulated as a local transport map: an initial flow policy augmented by a residual displacement. By analyzing the induced density transformation, we derive a local quadratic approximation of the KL-constrained objective governed by the Fisher information matrix, enabling a tractable anisotropic optimization formulation. By leveraging the score function embedded in the flow velocity, we obtain a corresponding quadratic constraint for efficient optimization. Our results reveal that the optimality gap in prior methods arises from their isotropic approximation. In contrast, our framework achieves a controllable approximation error within a provable neighborhood of the optimal solution. Extensive experiments demonstrate state-of-the-art performance across diverse offline RL benchmarks. See project page: https://github.com/ARC0127/Fisher-Decorator.

Xiaoyuan Cheng, Haoyu Wang, Wenxuan Yuan +4

University College London · Shanghai Jiao Tong University · Imperial College London +3

Flow MatchingOffline RLResidual Policy Learning
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Apr 20, 2026

OFlow: Injecting Object-Aware Temporal Flow Matching for Robust Robotic Manipulation

Robust robotic manipulation requires not only predicting how the scene evolves over time, but also recognizing task-relevant objects in complex scenes. However, existing VLA models face two limitations. They typically act only on the current frame, while future prediction and object-aware reasoning are often learned in separate latent spaces. We propose OFlow (injecting Object-Aware Temporal Flow Matching into VLAs), a framework that addresses both limitations by unifying temporal foresight and object-aware reasoning in a shared semantic latent space. Our method forecasts future latents with temporal flow matching, factorizes them into object-aware representations that emphasize physically relevant cues while filtering task-irrelevant variation, and conditions continuous action generation on these predictions. By integrating OFlow into VLA pipelines, our method enables more reliable control under distribution shifts. Extensive experiments across LIBERO, LIBERO-Plus, MetaWorld, and SimplerEnv benchmarks and real-world tasks demonstrate that object-aware foresight consistently enhances robustness and success.

Kuanning Wang, Ke Fan, Chenhao Qiu +5

Fudan University Shanghai, China · University of Southern California Los Angeles, CA, USA · KAUST Saudi Arabia

VLM RobustnessFlow MatchingObject-Centric Representation LearningRobotic ManipulationVision-Language-Action Models
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Apr 20, 2026

OmniVLA-RL: A Vision-Language-Action Model with Spatial Understanding and Online RL

Visual-Language-Action (VLA) models represent a paradigm shift in embodied AI, yet existing frameworks often struggle with imprecise spatial perception, suboptimal multimodal fusion, and instability in reinforcement learning. To bridge these gaps, we propose OmniVLA-RL, a novel architecture that leverages a Mix-of-Transformers (MoT) design to synergistically integrate reasoning, spatial, and action experts. Furthermore, we introduce Flow-GSPO, which reformulates flow matching as a Stochastic Differential Equation (SDE) process and integrates it with Group Segmented Policy Optimization (GSPO) to enhance action precision and training robustness. Extensive evaluations on the LIBERO and LIBERO-Plus benchmarks demonstrate that OmniVLA-RL achieves decent overall performance and surpasses mainstream existing methods, effectively overcoming the fundamental limitations of current VLA models.

Haoxiang Jie, Yaoyuan Yan, Xiangyu Wei +4

1AI Lab, Country Garden Services · 3VBot · 2Omni AI +1

Flow MatchingPolicy OptimizationRoboticsVision-Language-Action Models
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Apr 19, 2026

FlowC2S: Flowing from Current to Succeeding Frames for Fast and Memory-Efficient Video Continuation

This paper introduces a novel methodology for generating fast and memory-efficient video continuations. Our method, dubbed FlowC2S, fine-tunes a pre-trained text-to-video flow model to learn a vector field between the current and succeeding video chunks. Two design choices are key. First, we introduce inherent optimal couplings, utilizing temporally adjacent video chunks during training as a practical proxy for true optimal couplings, resulting in straighter flows. Second, we incorporate target inversion, injecting the inverted latent of the target chunk into the input representation to strengthen correspondences and improve visual fidelity. By flowing directly from current to succeeding frames, instead of the common combination of current frames with noise to generate a video continuation, we reduce the dimensionality of the model input by a factor of two. The proposed method, fine-tuned from LTXV and Wan, surpasses the state-of-the-art scores across quantitative evaluations with FID and FVD, with as few as five neural function evaluations.

Hovhannes Margaryan, Quentin Bammey, Christian Sandor

Team ARAI, Universit´e Paris-Saclay, CNRS, LISN, France · LTCI, T´el´ecom Paris, Institut Polytechnique de Paris, France

Flow MatchingT2V GenerationLong Video GenerationVideo GenerationVideo PredictionFlow-Based Generative Modeling
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Apr 18, 2026

FlowRefiner: Flow Matching-Based Iterative Refinement for 3D Turbulent Flow Simulation

Accurate autoregressive prediction of 3D turbulent flows remains challenging for neural PDE solvers, as small errors in fine-scale structures can accumulate rapidly over rollout. In this paper, we propose FlowRefiner, a flow matching-based iterative refinement framework for 3D turbulent flow simulation. The method replaces stochastic denoising refinement with deterministic ODE-based correction, uses a unified velocity-field regression objective across all refinement stages, and introduces a decoupled sigma schedule that fixes the noise range independently of refinement depth. These design choices yield stable and effective refinement in the small-noise regime. Experiments on large-scale 3D turbulence with rich multi-scale structures show that FlowRefiner achieves state-of-the-art autoregressive prediction accuracy and strong physical consistency. Although developed for turbulent flow simulation, the proposed framework is broadly applicable to iterative refinement problems in scientific modeling.

Yilong Dai, Yiming Sun, Yiheng Chen +3

University of Alabama · University of Pittsburgh

Flow MatchingNeural PDE SolversIterative RefinementComputational Fluid Dynamics
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Apr 18, 2026

Can We Build Scene Graphs, Not Classify Them? FlowSG: Progressive Image-Conditioned Scene Graph Generation with Flow Matching

Scene Graph Generation (SGG) unifies object localization and visual relationship reasoning by predicting boxes and subject-predicate-object triples. Yet most pipelines treat SGG as a one-shot, deterministic classification problem rather than a genuinely progressive, generative task. We propose FlowSG, which recasts SGG as continuous-time transport on a hybrid discrete-continuous state: starting from a noised graph, the model progressively grows an image-conditioned scene graph through constraint-aware refinements that jointly synthesize nodes (objects) and edges (predicates). Specifically, we first leverage a VQ-VAE to quantize a scene graph (e.g., continuous visual features) into compact, predictable tokens; a graph Transformer then (i) predicts a conditional velocity field to transport continuous geometry (boxes) and (ii) updates discrete posteriors for categorical tokens (object features and predicate labels), coupling semantics and geometry via flow-conditioned message aggregation. Training combines flow-matching losses for geometry with a discrete-flow objective for tokens, yielding few-step inference and plug-and-play compatibility with standard detectors and segmenters. Extensive experiments on VG and PSG under closed- and open-vocabulary protocols show consistent gains in predicate R/mR and graph-level metrics, validating the mixed discrete-continuous generative formulation over one-shot classification baselines, with an average improvement of about 3 points over the state-of-the-art USG-Par.

Xin Hu, Ke Qin, Wen Yin +3

The Laboratory of Intelligent Collaborative Computing of UESTC · Monash University · Guangdong Laboratory of Artificial Intelligence and Digital Economy (SZ)

Scene Graph GenerationFlow MatchingScene Graphs
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Apr 17, 2026

The Amazing Stability of Flow Matching

The success of deep generative models in generating high-quality and diverse samples is often attributed to particular architectures and large training datasets. In this paper, we investigate the impact of these factors on the quality and diversity of samples generated by flow-matching models. Surprisingly, in our experiments on CelebA-HQ dataset, flow matching remains stable even when pruning 50% of the dataset. That is, the quality and diversity of generated samples are preserved. Moreover, pruning impacts the latent representation only slightly, that is, samples generated by models trained on the full and pruned dataset map to visually similar outputs for a given seed. We observe similar stability when changing the architecture or training configuration, such that the latent representation is maintained under these changes as well. Our results quantify just how strong this stability can be in practice, and help explain the reliability of flow-matching models under various perturbations.

Rania Briq, Michael Kamp, Ohad Fried +2

Forschungszentrum Jülich · TU Dortmund · Lamarr Institute +4

Flow MatchingGenerative ModelingFlow-Based Generative Modeling
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Apr 16, 2026

Frequency-Aware Flow Matching for High-Quality Image Generation

Flow matching models have emerged as a powerful framework for realistic image generation by learning to reverse a corruption process that progressively adds Gaussian noise. However, because noise is injected in the latent domain, its impact on different frequency components is non-uniform. As a result, during inference, flow matching models tend to generate low-frequency components (global structure) in the early stages, while high-frequency components (fine details) emerge only later in the reverse process. Building on this insight, we propose Frequency-Aware Flow Matching (FreqFlow), a novel approach that explicitly incorporates frequency-aware conditioning into the flow matching framework via time-dependent adaptive weighting. We introduce a two-branch architecture: (1) a frequency branch that separately processes low- and high-frequency components to capture global structure and refine textures and edges, and (2) a spatial branch that synthesizes images in the latent domain, guided by the frequency branch's output. By explicitly integrating frequency information into the generation process, FreqFlow ensures that both large-scale coherence and fine-grained details are effectively modeled low-frequency conditioning reinforces global structure, while high-frequency conditioning enhances texture fidelity and detail sharpness. On the class-conditional ImageNet-256 generation benchmark, our method achieves state-of-the-art performance with an FID of 1.38, surpassing the prior diffusion model DiT and flow matching model SiT by 0.79 and 0.58 FID, respectively. Code is available at https://github.com/OliverRensu/FreqFlow.

Sucheng Ren, Qihang Yu, Ju He +3

Johns Hopkins University · ByteDance

Flow MatchingConditional Image GenerationImage GenerationFlow-Based Generative Modeling
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Apr 16, 2026

RelativeFlow: Taming Medical Image Denoising Learning with Noisy Reference

Medical image denoising (MID) lacks absolutely clean images for supervision, leading to a noisy reference problem that fundamentally limits denoising performance. Existing simulated-supervised discriminative learning (SimSDL) and simulated-supervised generative learning (SimSGL) treat noisy references as clean targets, causing suboptimal convergence or reference-biased learning, while self-supervised learning (SSL) imposes restrictive noise assumptions that are seldom satisfied in realistic MID scenarios. We propose RelativeFlow, a flow matching framework that learns from heterogeneous noisy references and drives inputs from arbitrary quality levels toward a unified high-quality target. RelativeFlow reformulates flow matching by decomposing the absolute noise-to-clean mapping into relative noisier-to-noisy mappings, and realizes this formulation through two key components: 1) consistent transport (CoT), a displacement map that constrains relative flows to be components of and progressively compose a unified absolute flow, and 2) simulation-based velocity field (SVF), which constructs a learnable velocity field using modality-specific degradation operators to support different medical imaging modalities. Extensive experiments on Computed Tomography (CT) and Magnetic Resonance (MR) denoising demonstrate that RelativeFlow significantly outperforms existing methods, taming MID with noisy references.

Yuxin Liu, Yiqing Dong, Wenxue Yu +4

School of Computer Science and Engineering, Southeast University, China · Department of Optical Sciences, University of Arizona, USA · School of Instrument Science and Engineering, Southeast University, China +1

Flow MatchingImage Denoising
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