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We introduce a new paradigm for generative modeling built on Continuous Normalizing Flows (CNFs), allowing us to train CNFs at unprecedented scale. Specifically, we present the notion of Flow Matching (FM), a simulation-free approach for…

Machine Learning · Computer Science 2023-02-09 Yaron Lipman , Ricky T. Q. Chen , Heli Ben-Hamu , Maximilian Nickel , Matt Le

Conditional flow matching (CFM) stands out as an efficient, simulation-free approach for training flow-based generative models, achieving remarkable performance for data generation. However, CFM is insufficient to ensure accuracy in…

Machine Learning · Computer Science 2026-02-03 Yuhao Huang , Taos Transue , Shih-Hsin Wang , William Feldman , Hong Zhang , Bao Wang

Recent efforts have extended the flow-matching framework to discrete generative modeling. One strand of models directly works with the continuous probabilities instead of discrete tokens, which we colloquially refer to as Continuous-State…

Machine Learning · Computer Science 2025-04-15 Chaoran Cheng , Jiahan Li , Jiajun Fan , Ge Liu

Flow matching models have shown great potential in image generation tasks among probabilistic generative models. However, most flow matching models in the literature do not explicitly utilize the underlying clustering structure in the…

Computer Vision and Pattern Recognition · Computer Science 2025-10-09 Anirban Samaddar , Yixuan Sun , Viktor Nilsson , Sandeep Madireddy

Flow matching (FM) is a family of training algorithms for fitting continuous normalizing flows (CNFs). Conditional flow matching (CFM) exploits the fact that the marginal vector field of a CNF can be learned by fitting least-squares…

Machine Learning · Statistics 2025-02-04 Ganchao Wei , Li Ma

This paper introduces a novel framework for image quality transfer based on conditional flow matching (CFM). Unlike conventional generative models that rely on iterative sampling or adversarial objectives, CFM learns a continuous flow…

Computer Vision and Pattern Recognition · Computer Science 2025-10-15 Huu Tien Nguyen , Ahmed Karam Eldaly

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…

Computer Vision and Pattern Recognition · Computer Science 2026-03-17 Chiensheng Chiang , Kuan-Hsun Tu , Jia-Wei Liao , Cheng-Fu Chou , Tsung-Wei Ke

We introduce Statistical Flow Matching (SFM), a novel and mathematically rigorous flow-matching framework on the manifold of parameterized probability measures inspired by the results from information geometry. We demonstrate the…

Machine Learning · Computer Science 2025-11-26 Chaoran Cheng , Jiahan Li , Jian Peng , Ge Liu

Generative models excel at synthesizing high-fidelity samples from complex data distributions, but they often violate hard constraints arising from physical laws or task specifications. A common remedy is to project intermediate samples…

Machine Learning · Computer Science 2025-09-30 Jinhao Liang , Yixuan Sun , Anirban Samaddar , Sandeep Madireddy , Ferdinando Fioretto

Conditional Flow Matching (CFM), a simulation-free method for training continuous normalizing flows, provides an efficient alternative to diffusion models for key tasks like image and video generation. The performance of CFM in solving…

Machine Learning · Computer Science 2026-03-17 Aram Davtyan , Leello Tadesse Dadi , Volkan Cevher , Paolo Favaro

Generative models have achieved remarkable progress with the emergence of flow matching (FM). It has demonstrated strong generative capabilities and attracted significant attention as a simulation-free flow-based framework capable of…

Computer Vision and Pattern Recognition · Computer Science 2026-04-01 Huynh Trinh Ngoc , Hoang Anh Nguyen Kim , Toan Nguyen Hai , Long Tran Quoc

Current discriminative depth estimation methods often produce blurry artifacts, while generative approaches suffer from slow sampling due to curvatures in the noise-to-depth transport. Our method addresses these challenges by framing depth…

Computer Vision and Pattern Recognition · Computer Science 2024-12-20 Ming Gui , Johannes Schusterbauer , Ulrich Prestel , Pingchuan Ma , Dmytro Kotovenko , Olga Grebenkova , Stefan Andreas Baumann , Vincent Tao Hu , Björn Ommer

Iterative generative models such as Flow Matching and Diffusion models have demonstrated strong test-time scaling behavior, where additional inference computation can improve generation quality. In contrast, Drift Models offer efficient…

Machine Learning · Computer Science 2026-05-19 Chenrui Ma , Xi Xiao , Lin Zhao , Tianyang Wang , Ferdinando Fioretto , Yanning Shen

In this work, we propose the Generative Latent Flow (GLF), an algorithm for generative modeling of the data distribution. GLF uses an Auto-encoder (AE) to learn latent representations of the data, and a normalizing flow to map the…

Computer Vision and Pattern Recognition · Computer Science 2019-09-24 Zhisheng Xiao , Qing Yan , Yali Amit

Flow matching casts sample generation as learning a continuous-time velocity field that transports noise to data. Existing flow matching networks typically predict each point's velocity independently, considering only its location and time…

Machine Learning · Computer Science 2025-11-11 Md Shahriar Rahim Siddiqui , Moshe Eliasof , Eldad Haber

We propose Pullback Flow Matching (PFM), a novel framework for generative modeling on data manifolds. Unlike existing methods that assume or learn restrictive closed-form manifold mappings for training Riemannian Flow Matching (RFM) models,…

Machine Learning · Computer Science 2025-07-10 Friso de Kruiff , Erik Bekkers , Ozan Öktem , Carola-Bibiane Schönlieb , Willem Diepeveen

Flow matching has recently emerged as a powerful alternative to diffusion models, providing a continuous-time formulation for generative modeling and representation learning. Yet, we show that this framework suffers from a fundamental…

Machine Learning · Computer Science 2025-09-26 Weili Zeng , Yichao Yan

Flow Matching (FM) has emerged as a powerful paradigm for continuous normalizing flows, yet standard FM implicitly performs an unweighted $L^2$ regression over the entire ambient space. In high dimensions, this leads to a fundamental…

Machine Learning · Statistics 2026-05-26 Shinto Eguchi

The goal of this paper is to provide a new perspective on speech modeling by incorporating perceptual invariances such as amplitude scaling and temporal shifts. Conventional generative formulations often treat each dataset sample as a fixed…

Audio and Speech Processing · Electrical Eng. & Systems 2025-12-24 Doyeop Kwak , Youngjoon Jang , Joon Son Chung

Standard flow matching scales well but typically relies on an unstructured source distribution, limiting its ability to learn interpretable latent structure. Latent-variable models, by contrast, capture structure but often sacrifice…

Machine Learning · Computer Science 2026-05-11 Xavier Sumba , Carles Balsells-Rodas , Yingzhen Li
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