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.

Mar 13, 2026

Mask2Flow-TSE: Two-Stage Target Speaker Extraction with Masking and Flow Matching

Target speaker extraction (TSE) extracts the target speaker's voice from overlapping speech given a reference utterance. Existing masking-based approaches are lightweight and effective but suffer from an inability to synthesize missing content, leading to degraded perceptual quality. On the other hand, recent generative TSE models typically synthesize high-quality speech with diffusion, but require numerous iterative steps resulting in high computational costs and latency. We propose Mask2Flow-TSE, a two-stage framework combining the strengths of both paradigms. We introduce the deletion/insertion (D/I) proportion, an analytical tool that reveals early flow steps predominantly remove signal components rather than synthesize them. Based on this finding, we decouple deletion from insertion: a masking-based module handles the deletion-dominant early steps, while a single flow-matching step performs the remaining insertion for high-quality reconstruction. Specifically, the first stage uses lightweight convolution for the masking module, while the second stage employs a Diffusion Transformer (DiT) adapted for TSE with speaker conditioning. Unlike prior approaches that start from Gaussian noise, our method starts from the masked spectrogram, enabling high-quality reconstruction in a single inference step. Experiments show that Mask2Flow-TSE produces high-quality extractions with only 85M parameters and one-step inference, while preserving clean single-speaker inputs with minimal degradation.

Junwon Moon, Seungbeom Kim, Hansol Park +4

Sungkyunkwan University · University of Seoul

Target Speaker ExtractionFlow MatchingSpeech ProcessingSpeech Enhancement
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Mar 13, 2026

Self-Flow-Matching assisted Full Waveform Inversion

Full-waveform inversion (FWI) is a high-resolution seismic imaging method that estimates subsurface velocity by matching simulated and recorded waveforms. However, FWI is highly nonlinear, prone to cycle skipping, and sensitive to noise, particularly when low frequencies are missing or the initial model is poor, leading to failures under imperfect acquisition. Diffusion-regularized FWI introduces generative priors to encourage geologically realistic models, but these priors typically require costly offline pretraining and can deteriorate under distribution shift. Moreover, they assume Gaussian initialization and a fixed noise schedule, in which it is unclear how to map a deterministic FWI iterate and its starting model to a well-defined diffusion time or noise level. To address these limitations, we introduce Self-Flow-Matching assisted Full-Waveform Inversion (SFM-FWI), a physics-driven framework that eliminates the need for large-scale offline pretraining while avoiding the noise-level alignment ambiguity. SFM-FWI leverages flow matching to learn a transport field without assuming Gaussian initialization or a predefined noise schedule, so the initial model can be used directly as the starting point of the dynamics. Our approach trains a single flow network online using the governing physics and observed data. At each outer iteration, we build an interpolated model and update the flow by backpropagating the FWI data misfit, providing self-supervision without external training pairs. Experiments on challenging synthetic benchmarks show that SFM-FWI delivers more accurate reconstructions, greater noise robustness, and more stable convergence than standard FWI and pretraining-free regularization methods.

Xinquan Huang, Paris Perdikaris

University of Pennsylvania

Inverse ProblemsPhysics-Informed Generative ModelingFlow Matching
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Mar 12, 2026

Curriculum Sampling: A Two-Phase Curriculum for Efficient Training of Flow Matching

Timestep sampling p(t)p(t) is a central design choice in Flow Matching models, yet common practice increasingly favors static middle-biased distributions (e.g., Logit-Normal). We show that this choice induces a speed--quality trade-off: middle-biased sampling accelerates early convergence but yields worse asymptotic fidelity than Uniform sampling. By analyzing per-timestep training losses, we identify a U-shaped difficulty profile with persistent errors near the boundary regimes, implying that under-sampling the endpoints leaves fine details unresolved. Guided by this insight, we propose Curriculum Sampling, a two-phase schedule that begins with middle-biased sampling for rapid structure learning and then switches to Uniform sampling for boundary refinement. On CIFAR-10, Curriculum Sampling improves the best FID from 3.853.85 (Uniform) to 3.223.22 while reaching peak performance at 100100k rather than 150150k training steps. Our results highlight that timestep sampling should be treated as an evolving curriculum rather than a fixed hyperparameter.

Pengwei Sun

Stanford University

Flow MatchingFlow-Based Generative ModelingCurriculum Learning
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Mar 12, 2026

EvoFlows: Evolutionary Edit-Based Flow-Matching for Protein Engineering

We introduce EvoFlows, a variable-length protein sequence-to-sequence modeling approach designed for protein engineering. Existing protein language models are poorly suited for optimization tasks: autoregressive models require full sequence generation, masked language and discrete diffusion models rely on pre-specified mutation locations, and no existing methods naturally support insertions and deletions relative to a template sequence. EvoFlows learns mutational trajectories between evolutionarily related protein sequences via edit flows, allowing it to perform a controllable number of mutations (insertions, deletions, and substitutions) on a template sequence, predicting not only which mutation to perform, but also where it should occur. Through extensive in silico evaluation on diverse protein families from UniRef and OAS, we show that EvoFlows generates variants that remain consistent with natural protein families while exploring farther from template sequences than leading baselines.

Nicolas Deutschmann, Constance Ferragu, Jonathan D. Ziegler +2

Cradle

Protein DesignSequence ModelingFlow-Based Generative ModelingFlow Matching
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Mar 11, 2026

The Quadratic Geometry of Flow Matching: Semantic Granularity Alignment for Text-to-Image Synthesis

In this work, we analyze the optimization dynamics of generative fine-tuning. We observe that under the Flow Matching framework, the standard MSE objective can be formulated as a Quadratic Form governed by a dynamically evolving Neural Tangent Kernel (NTK). This geometric perspective reveals a latent Data Interaction Matrix, where diagonal terms represent independent sample learning and off-diagonal terms encode residual correlation between heterogeneous features. Although standard training implicitly optimizes these cross-term interferences, it does so without explicit control; moreover, the prevailing data-homogeneity assumption may constrain the model's effective capacity. Motivated by this insight, we propose Semantic Granularity Alignment (SGA), using Text-to-Image synthesis as a testbed. SGA engineers targeted interventions in the vector residual field to mitigate gradient conflicts. Evaluations across DiT and U-Net architectures confirm that SGA advances the efficiency-quality trade-off by accelerating convergence and improving structural integrity.

Zhinan Xiong, Shunqi Yuan

Conservatoire National des Arts et Métiers, Paris, France · Sun Yat-sen University, Guangzhou, China

Flow MatchingT2I Generation
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Mar 11, 2026

COT-FM: Cluster-wise Optimal Transport Flow Matching

We introduce COT-FM, a general framework that reshapes the probability path in Flow Matching (FM) to achieve faster and more reliable generation. FM models often produce curved trajectories due to random or batchwise couplings, which increase discretization error and reduce sample quality. COT-FM fixes this by clustering target samples and assigning each cluster a dedicated source distribution obtained by reversing pretrained FM models. This divide-and-conquer strategy yields more accurate local transport and significantly straighter vector fields, all without changing the model architecture. As a plug-and-play approach, COT-FM consistently accelerates sampling and improves generation quality across 2D datasets, image generation benchmarks, and robotic manipulation tasks.

Chiensheng Chiang, Kuan-Hsun Tu, Jia-Wei Liao +2

National Taiwan University

Flow MatchingGenerative ModelingFlow-Based Generative ModelingImage GenerationOptimal Transport
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Mar 11, 2026

AlphaFlowTSE: One-Step Generative Target Speaker Extraction via Conditional AlphaFlow

In target speaker extraction (TSE), we aim to recover target speech from a multi-talker mixture using a short enrollment utterance as reference. Recent studies on diffusion and flow-matching generators have improved target-speech fidelity. However, multi-step sampling increases latency, and one-step solutions often rely on a mixture-dependent time coordinate that can be unreliable for real-world conversations. We present AlphaFlowTSE, a one-step conditional generative model trained with a Jacobian-vector product (JVP)-free AlphaFlow objective. AlphaFlowTSE learns mean-velocity transport along a mixture-to-target trajectory starting from the observed mixture, eliminating auxiliary mixing-ratio prediction, and stabilizes training by combining flow matching with an interval-consistency teacher-student target. Experiments on Libri2Mix and REAL-T confirm that AlphaFlowTSE improves target-speaker similarity and real-mixture generalization for downstream automatic speech recognition (ASR).

Duojia Li, Shuhan Zhang, Zihan Qian +5

School of Electronic Science and Engineering, Xiamen University, Xiamen, China · Shenzhen Loop Area Institute, Shenzhen, China · School of Artificial Intelligence, The Chinese University of Hong Kong, Shenzhen, Shenzhen, China +3

Target Speaker ExtractionOne-Step Generative ModelingFlow Matching
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Mar 11, 2026

VeloEdit: Training-Free Consistent and Continuous Instruction-Based Image Editing via Velocity Field Decomposition

Instruction-based image editing aims to modify source content according to textual instructions. However, existing methods built upon flow matching often struggle to maintain consistency in non-edited regions due to denoising-induced reconstruction errors that cause drift in preserved content. Moreover, they typically lack fine-grained control over edit strength. To address these limitations, we propose VeloEdit, a training-free method that enables highly consistent and continuously controllable editing. VeloEdit dynamically identifies editing regions by quantifying the discrepancy between the velocity fields responsible for preserving source content and those driving the desired edits. Based on this partition, we enforce consistency in preservation regions by substituting the editing velocity with the source-restoring velocity, while enabling continuous modulation of edit intensity in target regions via velocity interpolation. Unlike prior works that rely on complex attention manipulation or auxiliary trainable modules, VeloEdit operates directly on the velocity fields. Extensive experiments on Flux.1 Kontext and Qwen-Image-Edit demonstrate that VeloEdit improves visual consistency and editing continuity with negligible additional computational cost. Code is available at https://github.com/xmulzq/VeloEdit.

Zongqing Li, Zhihui Liu, Yujie Xie +3

Xiamen University · Truesight

Training-Free Image EditingImage EditingText-Guided Image EditingFlow Matching
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Mar 9, 2026

The Coupling Within: Flow Matching via Distilled Normalizing Flows

Flow models have rapidly become the go-to method for training and deploying large-scale generators, owing their success to inference-time flexibility via adjustable integration steps. A crucial ingredient in flow training is the choice of coupling measure for sampling noise/data pairs that define the flow matching (FM) regression loss. While FM training defaults usually to independent coupling, recent works show that adaptive couplings informed by noise/data distributions (e.g., via optimal transport, OT) improve both model training and inference. We radicalize this insight by shifting the paradigm: rather than computing adaptive couplings directly, we use distilled couplings from a different, pretrained model capable of placing noise and data spaces in bijection -- a property intrinsic to normalizing flows (NF) through their maximum likelihood and invertibility requirements. Leveraging recent advances in NF image generation via auto-regressive (AR) blocks, we propose Normalized Flow Matching (NFM), a new method that distills the quasi-deterministic coupling of pretrained NF models to train student flow models. These students achieve the best of both worlds: significantly outperforming flow models trained with independent or even OT couplings, while also improving on the teacher AR-NF model.

David Berthelot, Tianrong Chen, Jiatao Gu +6

Flow-Based Generative ModelingFlow MatchingNormalizing Flows
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Mar 9, 2026

Statistical Inference via Generative Models: Flow Matching and Causal Inference

Generative AI has achieved remarkable empirical success, but from the perspective of statistics it often remains opaque: its predictions may be accurate, yet the underlying mechanism is difficult to interpret, analyze, and trust. This book reinterprets generative AI in the language of statistics, using flow matching as a central example. The key idea is that generative models should be understood not merely as devices for producing plausible data, but as methods for the nonparametric learning of high-dimensional probability distributions. From this viewpoint, missing-data imputation becomes principled sampling from learned conditional distributions, counterfactual analysis becomes the estimation of intervention distributions, and distributional dynamics become statistically analyzable objects. Mathematically, flow matching represents distributional deformation through the continuity equation and a time-dependent velocity field, thereby extending score matching from the learning of static score fields to the learning of transport paths themselves. Building on this foundation, the book develops a statistical framework in which generative models are used to estimate nuisance components while inferential validity is maintained through orthogonalization and cross-fitting in the spirit of double/debiased machine learning. Applications to survival analysis, censoring, missingness, and causal inference show how generative models can be integrated into statistical inference for structured high-dimensional problems.

Shinto Eguchi

Causal InferenceFlow MatchingFlow-Based Generative Modeling
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Mar 6, 2026

Self-Supervised Flow Matching for Scalable Multi-Modal Synthesis

Strong semantic representations improve the convergence and generation quality of diffusion and flow models. Existing approaches largely rely on external models, which require separate training, operate on misaligned objectives, and exhibit unexpected scaling behavior. We argue that this dependence arises from the model's training objective, which poses a denoising task with little incentive to learn semantic representations. We introduce Self-Flow: a self-supervised flow matching paradigm that integrates representation learning within the generative framework. Our key mechanism, Dual-Timestep Scheduling, applies heterogeneous noise levels across tokens, creating an information asymmetry that forces the model to infer missing information from corrupted inputs. This drives learning strong representations alongside generative capabilities without external supervision. Our method generalizes across modalities and enables multi-modal training while following expected scaling laws, achieving superior image, video, and audio generation.

Hila Chefer, Patrick Esser, Dominik Lorenz +5

Black Forest Labs · MIT

Flow-Based Generative ModelingFlow MatchingMultimodal GenerationSelf-Supervised Learning
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Mar 6, 2026

Training Flow Matching: The Role of Weighting and Parameterization

We study the training objectives of denoising-based generative models, with a particular focus on loss weighting and output parameterization, including noise-, clean image-, and velocity-based formulations. Through a systematic numerical study, we analyze how these training choices interact with the intrinsic dimensionality of the data manifold, model architecture, and dataset size. Our experiments span synthetic datasets with controlled geometry as well as image data, and compare training objectives using quantitative metrics for denoising accuracy (PSNR across noise levels) and generative quality (FID). Rather than proposing a new method, our goal is to disentangle the various factors that matter when training a flow matching model, in order to provide practical insights on design choices.

Anne Gagneux, Ségolène Martin, Rémi Gribonval +1

ENS de Lyon, CNRS, Universit´e Claude Bernard Lyon 1, Inria, LIP, UMR 5668, France · Technische Universität Berlin, Germany · Inria, ENS de Lyon, CNRS, Universit´e Claude Bernard Lyon 1, LIP, UMR 5668, France

Flow MatchingAdaptive Loss WeightingFlow-Based Generative ModelingDiffusion Models
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Mar 6, 2026

Reflective Flow Sampling Enhancement

The growing demand for text-to-image generation has led to rapid advances in generative modeling. Recently, text-to-image diffusion models trained with flow matching algorithms, such as FLUX, have achieved remarkable progress and emerged as strong alternatives to conventional diffusion models. At the same time, inference-time enhancement strategies have been shown to improve the generation quality and text-prompt alignment of text-to-image diffusion models. However, these techniques are mainly applicable to conventional diffusion models and usually fail to perform well on flow models. To bridge this gap, we propose Reflective Flow Sampling (RF-Sampling), a theoretically-grounded and training-free inference enhancement framework explicitly designed for flow models, especially for the CFG-distilled variants (i.e., models distilled from CFG guidance techniques), like FLUX. Departing from heuristic interpretations, we provide a formal derivation proving that RF-Sampling implicitly performs gradient ascent on the text-image alignment score. By leveraging a linear combination of textual representations and integrating them with flow inversion, RF-Sampling allows the model to explore noise spaces that are more consistent with the input prompt. Extensive experiments across multiple benchmarks demonstrate that RF-Sampling consistently improves both generation quality and prompt alignment. Moreover, RF-Sampling is also the first inference enhancement method that can exhibit test-time scaling ability to some extent on FLUX.

Zikai Zhou, Muyao Wang, Shitong Shao +4

The Hong Kong University of Science and Technology (Guangzhou), Guangzhou, China. · The University of Tokyo, Japan. · Microsoft, Beijing. +1

T2I Diffusion ModelsFlow-Based Generative ModelingDiffusion Model GuidanceText-Image AlignmentFlow Matching
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Mar 4, 2026

Balancing Fidelity, Utility, and Privacy in Synthetic Cardiac MRI Generation: A Comparative Study

Deep learning in cardiac MRI (CMR) is fundamentally constrained by both data scarcity and privacy regulations. This study systematically benchmarks three generative architectures: Denoising Diffusion Probabilistic Models (DDPM), Latent Diffusion Models (LDM), and Flow Matching (FM) for synthetic CMR generation. Utilizing a two-stage pipeline where anatomical masks condition image synthesis, we evaluate generated data across three critical axes: fidelity, utility, and privacy. Our results show that diffusion-based models, particularly DDPM, provide the most effective balance between downstream segmentation utility, image fidelity, and privacy preservation under limited-data conditions, while FM demonstrates promising privacy characteristics with slightly lower task-level performance. These findings quantify the trade-offs between cross-domain generalization and patient confidentiality, establishing a framework for safe and effective synthetic data augmentation in medical imaging.

Madhura Edirisooriya, Dasuni Kawya, Ishan Kumarasinghe +5

University of Peradeniya, Sri Lanka · University of Maryland, College Park, USA · Tulane University School of Medicine, USA; Simula Research Laboratory, Norway +1

Medical Image SynthesisSynthetic Data AugmentationSynthetic Data EvaluationCardiac MRIPrivacy-Preserving MLFlow Matching
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Mar 4, 2026

Linearized Coupling Flow with Shortcut Constraints for One-Step Face Restoration

Face restoration can be formulated as a continuous-time transformation between image distributions via Flow Matching (FM). However, standard FM typically employs independent coupling, ignoring the statistical correlation between low-quality (LQ) and high-quality (HQ) data. This leads to intersecting trajectories and high velocity-field curvature, requiring multi-step integration. We propose Shortcut-constrained Coupling Flow for Face Restoration (SCFlowFR) to address these challenges. By establishing a data-dependent coupling, we explicitly model the LQ-HQ dependency to minimize path crossovers and promote near-linear probability flow. Furthermore, we employ a conditional mean estimator to refine the source distribution's anchor, effectively tightening the transport cost and stabilizing the velocity field. To ensure stable one-step inference, a shortcut constraint is introduced to supervise average velocities over arbitrary intervals, mitigating discretization bias in large-step updates. SCFlowFR achieves state-of-the-art one-step restoration, providing a superior trade-off between perceptual fidelity and computational efficiency.

Xiaohui Sun, Hanlin Wu

School of Information Science and Technology, Beijing Foreign Studies University, Beijing 100089, China

Image RestorationFlow MatchingFlow-Based Generative ModelingOne-Step Generative Modeling
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Mar 2, 2026

Preconditioned Flow Matching

Flow matching (FM) learns vector fields by regressing stochastic velocity targets along intermediate distributions ptp_t. We identify a geometric optimization bottleneck in this regression problem: when the covariance ΣtΣ_t of ptp_t is ill-conditioned, gradient-based training rapidly fits high-variance directions while making slow progress along low-variance ones. In an exactly solvable Gaussian setting, we prove that the excess risk is weighted by ΣtΣ_t, and that both gradient descent and stochastic gradient descent inherit condition-number-dependent convergence. We then extend the analysis to Gaussian mixtures, showing that multimodality does not average away this effect; instead, the slowest and worst-conditioned component can control optimization. Motivated by this analysis, we propose preconditioned flow matching\textit{preconditioned flow matching}, a precondition-then-match framework that transforms the target distribution into a more isotropic representation, trains the main flow in the transformed space, and maps generated samples back through the inverse transformation. We show theoretically that preconditioning reshapes the intermediate FM path and improves its conditioning. Across controlled Gaussian and Gaussian-mixture experiments, latent MNIST and other high resolution image datasets up to 512×512512{\times}512 resolution, preconditioning improves path-conditioning diagnostics, low-eigenvalue recovery, FID, MMD, precision, and recall. Compute-matched baselines and preconditioner-quality ablations further show that the gains are not explained merely by additional preconditioner parameters, but by improved geometry of the downstream flow matching problem. GitHub: https://github.com/ahxmeds/preconditioned-flow-matching.git.

Shadab Ahamed, Eshed Gal, Md Shahriar Rahim Siddiqui +3

University of British Columbia, Vancouver, Canada · University of Cambridge, Cambridge, United Kingdom

Flow MatchingFlow-Based Generative Modeling
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Mar 1, 2026

Flow Matching-enabled Test-Time Refinement for Unsupervised Cardiac MR Registration

Diffusion-based unsupervised image registration has been explored for cardiac cine MR, but expensive multi-step inference limits practical use. We propose FlowReg, a flow-matching framework in displacement field space that achieves strong registration in as few as two steps and supports further refinement with more steps. FlowReg uses warmup-reflow training: a single-step network first acts as a teacher, then a student learns to refine from arbitrary intermediate states, removing the need for a pre-trained model as in existing methods. An Initial Guess strategy feeds back the model prediction as the next starting point, improving refinement from step two onward. On ACDC and MM2 across six tasks (including cross-dataset generalization), FlowReg outperforms the state of the art on five tasks (+0.6% mean Dice score on average), with the largest gain in the left ventricle (+1.09%), and reduces LVEF estimation error on all six tasks (-2.58 percentage points), using only 0.7% extra parameters and no segmentation labels. Code is available at https://github.com/mathpluscode/FlowReg.

Yunguan Fu, Wenjia Bai, Wen Yan +3

University College London · InstaDeep · Imperial College London

Medical Image RegistrationDeformable Image RegistrationCardiac MRIFlow Matching
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Mar 1, 2026

GeodesicNVS: Probability Density Geodesic Flow Matching for Novel View Synthesis

Recent advances in generative modeling have substantially enhanced novel view synthesis, yet maintaining consistency across viewpoints remains challenging. Diffusion-based models rely on stochastic noise-to-data transitions, which obscure deterministic structures and yield inconsistent view predictions. We advocate a Data-to-Data Flow Matching framework that learns deterministic transformations between paired views, enhancing view-consistent synthesis through explicit data coupling. Building on this, we propose Probability Density Geodesic Flow Matching (PDG-FM), which aligns interpolation trajectories with density-based geodesics of a data manifold. To enable tractable geodesic estimation, we employ a teacher-student framework that distills density-based geodesic interpolants into an efficient ambient-space predictor. Empirically, our method surpasses diffusion-based baselines on Objaverse and GSO30 datasets, demonstrating improved structural coherence and smoother transitions across views. These results highlight the advantages of incorporating data-dependent geometric regularization into deterministic flow matching for consistent novel view generation.

Xuqin Wang, Tao Wu, Yanfeng Zhang +5

Huawei Hilbert Research Center (Dresden) · Technical University of Munich · Karlsruhe University of Applied Sciences

Novel View SynthesisFlow MatchingMulti-View Consistency
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Mar 1, 2026

AG-REPA: Causal Layer Selection for Representation Alignment in Audio Flow Matching

REPresentation Alignment (REPA) improves the training of generative flow models by aligning intermediate hidden states with pretrained teacher features, but its effectiveness in token-conditioned audio Flow Matching critically depends on the choice of supervised layers, which is typically made heuristically based on the depth. In this work, we introduce Attribution-Guided REPresentation Alignment (AG-REPA), a novel causal layer selection strategy for representation alignment in audio Flow Matching. Firstly, we find that layers that best store semantic/acoustic information (high teacher-space similarity) are not necessarily the layers that contribute most to the velocity field that drives generation, and we call it Store-Contribute Dissociation (SCD). To turn this insight into an actionable training guidance, we propose a forward-only gate ablation (FoG-A) that quantifies each layer's causal contribution via the induced change in the predicted velocity field, enabling sparse layer selection and adaptive weighting for alignment. Across unified speech and general-audio training (LibriSpeech + AudioSet) under different token-conditioning topologies, AG-REPA consistently outperforms REPA baselines. Overall, our results show that alignment is most effective when applied to the causally dominant layers that drive the velocity field, rather than to layers that are representationally rich but functionally passive.

Pengfei Zhang, Tianxin Xie, Minghao Yang +1

AI Thrust, Information Hub, The Hong Kong University of Science and Technology (Guangzhou).

Flow-Based Generative ModelingFlow MatchingAudio Representation LearningFeature Attribution
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Feb 28, 2026

RAFM: Retrieval-Augmented Flow Matching for Unpaired CBCT-to-CT Translation

Cone-beam CT (CBCT) is routinely acquired in radiotherapy but suffers from severe artifacts and unreliable Hounsfield Unit (HU) values, limiting its direct use for dose calculation. Synthetic CT (sCT) generation from CBCT is therefore an important task, yet paired CBCT--CT data are often unavailable or unreliable due to temporal gaps, anatomical variation, and registration errors. In this work, we introduce rectified flow (RF) into unpaired CBCT-to-CT translation in medical imaging. Although RF is theoretically compatible with unpaired learning through distribution-level coupling and deterministic transport, its practical effectiveness under small medical datasets and limited batch sizes remains underexplored. Direct application with random or batch-local pseudo pairing can produce unstable supervision due to semantically mismatched endpoint samples. To address this challenge, we propose Retrieval-Augmented Flow Matching (RAFM), which adapts RF to the medical setting by constructing retrieval-guided pseudo pairs using a frozen DINOv3 encoder and a global CT memory bank. This strategy improves empirical coupling quality and stabilizes unpaired flow-based training. Experiments on SynthRAD2023 under a strict subject-level true-unpaired protocol show that RAFM outperforms existing methods across FID, MAE, SSIM, PSNR, and SegScore. The code is available at https://github.com/HiLab-git/RAFM.git.

Xianhao Zhou, Jianghao Wu, Lanfeng Zhong +4

School of Mechanical and Electrical Engineering, University of Electronic Science and Technology of China, Chengdu, China · Faculty of Information Technology, Monash University, Melbourne, VIC 3800, Australia · Shanghai Artificial Intelligence Laboratory, Shanghai, China

Medical Image SynthesisImage-to-Image TranslationUnpaired Image-to-Image TranslationFlow MatchingCone-Beam CTRectified Flow
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Feb 27, 2026

Efficient Flow Matching for Sparse-View CT Reconstruction

Generative models, particularly Diffusion Models (DM), have shown strong potential for Computed Tomography (CT) reconstruction serving as expressive priors for solving ill-posed inverse problems. However, diffusion-based reconstruction relies on Stochastic Differential Equations (SDEs) for forward diffusion and reverse denoising, where such stochasticity can interfere with repeated data consistency corrections in CT reconstruction. Since CT reconstruction is often time-critical in clinical and interventional scenarios, improving reconstruction efficiency is essential. In contrast, Flow Matching (FM) models sampling as a deterministic Ordinary Differential Equation (ODE), yielding smooth trajectories without stochastic noise injection. This deterministic formulation is naturally compatible with repeated data consistency operations. Furthermore, we observe that FM-predicted velocity fields exhibit strong correlations across adjacent steps. Motivated by this, we propose an FM-based CT reconstruction framework (FMCT) and an efficient variant (EFMCT) that reuses previously predicted velocity fields over consecutive steps to substantially reduce the number of Neural network Function Evaluations (NFEs), thereby improving inference efficiency. We provide theoretical analysis showing that the error introduced by velocity reuse is bounded when combined with data consistency operations. Extensive experiments demonstrate that FMCT/EFMCT achieve competitive reconstruction quality while significantly improving computational efficiency compared with diffusion-based methods. The codebase is open-sourced at https://github.com/EFMCT/EFMCT.

Jiayang Shi, Lincen Yang, Zhong Li +3

Centrum Wiskunde en Informatica · LIACS, Leiden University · Great Bay University +1

Flow MatchingSparse-View CT ReconstructionComputational ImagingComputed Tomography
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Feb 25, 2026

Flow Matching is Adaptive to Manifold Structures

Flow matching has emerged as a simulation-free alternative to diffusion-based generative modeling, producing samples by solving an ODE whose time-dependent velocity field is learned along an interpolation between a simple source distribution (e.g., a standard normal) and a target data distribution. Flow-based methods often exhibit greater training stability and have achieved strong empirical performance in high-dimensional settings where data concentrate near a low-dimensional manifold, such as text-to-image synthesis, video generation, and molecular structure generation. Despite this success, existing theoretical analyses of flow matching assume target distributions with smooth, full-dimensional densities, leaving its effectiveness in manifold-supported settings largely unexplained. To this end, we theoretically analyze flow matching with linear interpolation when the target distribution is supported on a smooth manifold. We establish a non-asymptotic convergence guarantee for the learned velocity field, and then propagate this estimation error through the ODE to obtain statistical consistency of the implicit density estimator induced by the flow-matching objective. The resulting convergence rate is near minimax-optimal, depends only on the intrinsic dimension, and reflects the smoothness of both the manifold and the target distribution. Together, these results provide a principled explanation for how flow matching adapts to intrinsic data geometry and circumvents the curse of dimensionality.

Shivam Kumar, Yixin Wang, Lizhen Lin

Booth School of Business, University of Chicago · Department of Statistics, University of Michigan · Department of Mathematics, University of Maryland, College Park

Flow MatchingGenerative ModelingFlow-Based Generative ModelingStatistical Learning Theory
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Feb 25, 2026

Entropy-Controlled Flow Matching

Modern vision generators transport a base distribution to data through time-indexed measures, implemented as deterministic flows (ODEs) or stochastic diffusions (SDEs). Despite strong empirical performance, standard flow-matching objectives do not directly control the information geometry of the trajectory, allowing low-entropy bottlenecks that can transiently deplete semantic modes. We propose Entropy-Controlled Flow Matching (ECFM): a constrained variational principle over continuity-equation paths enforcing a global entropy-rate budget d/dt H(mu_t) >= -lambda. ECFM is a convex optimization in Wasserstein space with a KKT/Pontryagin system, and admits a stochastic-control representation equivalent to a Schrodinger bridge with an explicit entropy multiplier. In the pure transport regime, ECFM recovers entropic OT geodesics and Gamma-converges to classical OT as lambda -> 0. We further obtain certificate-style mode-coverage and density-floor guarantees with Lipschitz stability, and construct near-optimal collapse counterexamples for unconstrained flow matching.

Chika Maduabuchi

William & Mary, Williamsburg, VA, USA

Flow MatchingFlow-Based Generative ModelingEntropy RegularizationOptimal Transport
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Feb 25, 2026

D-Flow SGLD: Source-Space Posterior Sampling for Scientific Inverse Problems with Flow Matching

Data assimilation and scientific inverse problems require reconstructing high-dimensional physical states from sparse and noisy observations, ideally with uncertainty-aware posterior samples that remain faithful to learned priors and governing physics. While training-free conditional generation is well developed for diffusion models, corresponding conditioning and posterior sampling strategies for Flow Matching (FM) priors remain comparatively under-explored, especially on scientific benchmarks where fidelity must be assessed beyond measurement misfit. In this work, we study training-free conditional generation for scientific inverse problems under FM priors and organize existing inference-time strategies by where measurement information is injected: (i) guided transport dynamics that perturb sampling trajectories using likelihood information, and (ii) source-distribution inference that performs posterior inference over the source variable while keeping the learned transport fixed. Building on the latter, we propose D-Flow SGLD, a source-space posterior sampling method that augments differentiable source inference with preconditioned stochastic gradient Langevin dynamics, enabling scalable exploration of the source posterior induced by new measurement operators without retraining the prior or modifying the learned FM dynamics. We benchmark representative methods from both families on a hierarchy of problems: 2D toy posteriors, chaotic Kuramoto-Sivashinsky trajectories, and wall-bounded turbulence reconstruction. Across these settings, we quantify trade-offs among measurement assimilation, posterior diversity, and physics/statistics fidelity, and establish D-Flow SGLD as a practical FM-compatible posterior sampler for scientific inverse problems.

Meet Hemant Parikh, Yaqin Chen, Jian-Xun Wang

Sibley School of Mechanical and Aerospace Engineering, Cornell University, Ithaca, NY, USA · Department of Aerospace and Mechanical Engineering, University of Notre Dame, Notre Dame, IN, USA

Posterior SamplingBayesian Inverse ProblemsData AssimilationFlow MatchingStochastic Gradient Langevin Dynamics
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Feb 23, 2026

Laplacian Multi-scale Flow Matching for Generative Modeling

In this paper, we present Laplacian multiscale flow matching (LapFlow), a novel framework that enhances flow matching by leveraging multi-scale representations for image generative modeling. Our approach decomposes images into Laplacian pyramid residuals and processes different scales in parallel through a mixture-of-transformers (MoT) architecture with causal attention mechanisms. Unlike previous cascaded approaches that require explicit renoising between scales, our model generates multi-scale representations in parallel, eliminating the need for bridging processes. The proposed multi-scale architecture not only improves generation quality but also accelerates the sampling process and promotes scaling flow matching methods. Through extensive experimentation on CelebA-HQ and ImageNet, we demonstrate that our method achieves superior sample quality with fewer GFLOPs and faster inference compared to single-scale and multi-scale flow matching baselines. The proposed model scales effectively to high-resolution generation (up to 1024×\times1024) while maintaining lower computational overhead.

Zelin Zhao, Petr Molodyk, Haotian Xue +1

Georgia Institute of Technology Atlanta, GA 30332, USA

Mixture-of-TransformersGenerative ModelingFlow-Based Generative ModelingFlow Matching
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Feb 22, 2026

AdsorbFlow: energy-conditioned flow matching enables fast and realistic adsorbate placement

Identifying low-energy adsorption geometries on catalytic surfaces is a practical bottleneck for computational heterogeneous catalysis: the difficulty lies not only in the cost of density functional theory (DFT) but in proposing initial placements that relax into the correct energy basins. Conditional denoising diffusion has improved success rates, yet requires ∼\sim100 iterative steps per sample. Here we introduce AdsorbFlow, a deterministic generative model that learns an energy-conditioned vector field on the rigid-body configuration space of adsorbate translation and rotation via conditional flow matching. Energy information enters through classifier-free guidance conditioning -- not energy-gradient guidance -- and sampling reduces to integrating an ODE in as few as 5 steps. On OC20-Dense with full DFT single-point verification, AdsorbFlow with an EquiformerV2 backbone achieves 61.4% SR@10 and 34.1% SR@1 -- surpassing AdsorbDiff (31.8% SR@1, 41.0% SR@10) at every evaluation level and AdsorbML (47.7% SR@10) -- while using 20 times fewer generative steps and achieving the lowest anomaly rate among generative methods (6.8%). On 50 out-of-distribution systems, AdsorbFlow retains 58.0% SR@10 with a MLFF-to-DFT gap of only 4~percentage points. These results establish that deterministic transport is both faster and more accurate than stochastic denoising for adsorbate placement.

Jiangjie Qiu, Wentao Li, Honghao Chen +2

Beijing Key Laboratory of Artificial Intelligence for Advanced Chemical Engineering Materials, Department of Chemical Engineering, Tsinghua University, Beijing, China.

Flow-Based Generative ModelingMaterials ScienceFlow Matching
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Feb 20, 2026

Flow Matching with Injected Noise for Offline-to-Online Reinforcement Learning

Generative models have recently demonstrated remarkable success across diverse domains, motivating their adoption as expressive policies in reinforcement learning (RL). While they have shown strong performance in offline RL, particularly where the target distribution is well defined, their extension to online fine-tuning has largely been treated as a direct continuation of offline pre-training, leaving key challenges unaddressed. In this paper, we propose Flow Matching with Injected Noise for Offline-to-Online RL (FINO), a novel method that leverages flow matching-based policies to enhance sample efficiency for offline-to-online RL. FINO facilitates effective exploration by injecting noise into policy training, thereby encouraging a broader range of actions beyond those observed in the offline dataset. In addition to exploration-enhanced flow policy training, we combine an entropy-guided sampling mechanism to balance exploration and exploitation, allowing the policy to adapt its behavior throughout online fine-tuning. Experiments across diverse, challenging tasks demonstrate that FINO consistently achieves superior performance under limited online budgets.

Yongjae Shin, Jongseong Chae, Jongeui Park +1

KAIST

Offline-To-Online RLSample-Efficient RLRL ExplorationFlow Matching
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Feb 20, 2026

Balancing Symmetry and Efficiency in Graph Flow Matching

Equivariance is central to graph generative models, as it ensures the model respects the permutation symmetry of graphs. However, strict equivariance can increase computational cost due to added architectural constraints, and can slow down convergence because the model must be consistent across a large space of possible node permutations. We study this trade-off for graph generative models. Specifically, we start from an equivariant discrete flow-matching model, and relax its equivariance during training via a controllable symmetry modulation scheme based on sinusoidal positional encodings and node permutations. Experiments first show that symmetry-breaking can accelerate early training by providing an easier learning signal, but at the expense of encouraging shortcut solutions that can cause overfitting, where the model repeatedly generates graphs that are duplicates of the training set. On the contrary, properly modulating the symmetry signal can delay overfitting while accelerating convergence, allowing the model to reach stronger performance with 19%19\% of the baseline training epochs.

Benjamin Honoré, Alba Carballo-Castro, Yiming Qin +1

LTS4, EPFL, Lausanne, Switzerland

Generative ModelingEquivariant GNNsFlow MatchingEquivariant Representation LearningDiscrete Flow Matching
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Feb 20, 2026

Correlation Analysis of Generative Models

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

Zhengguo Li, Chaobing Zheng, Wei Wang

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

Generative ModelingDiffusion ModelsFlow Matching
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Feb 19, 2026

Variational Grey-Box Dynamics Matching

Deep generative models such as flow matching and diffusion models have shown great potential in learning complex distributions and dynamical systems, but often act as black-boxes, neglecting underlying physics. In contrast, physics-based simulation models described by ODEs/PDEs remain interpretable, but may have missing or unknown terms, unable to fully describe real-world observations. We bridge this gap with a novel grey-box method that integrates incomplete physics models directly into generative models. Our approach learns dynamics from observational trajectories alone, without ground-truth physics parameters, in a simulation-free manner that avoids scalability and stability issues of Neural ODEs. The core of our method lies in modelling a structured variational distribution within the flow matching framework, by using two latent encodings: one to model the missing stochasticity and multi-modal velocity, and a second to encode physics parameters as a latent variable with a physics-informed prior. Furthermore, we present an adaptation of the framework to handle second-order dynamics. Our experiments on representative ODE/PDE problems and real-world weather forecasting demonstrate that our method performs on par with or superior to fully data-driven approaches and previous grey-box baselines, while preserving the interpretability of the physics model. Our code is available at https://github.com/DMML-Geneva/VGB-DM.

Gurjeet Sangra Singh, Frantzeska Lavda, Giangiacomo Mercatali +1

Physics-Informed Generative ModelingSystem IdentificationFlow Matching
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