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Flow Matching (FM) is a recent generative modelling technique: we aim to learn how to sample from distribution $\mathfrak{X}_1$ by flowing samples from some distribution $\mathfrak{X}_0$ that is easy to sample from. The key trick is that…

Differential Geometry · Mathematics 2025-10-24 Finn M. Sherry , Bart M. N. Smets

We propose Functional Flow Matching (FFM), a function-space generative model that generalizes the recently-introduced Flow Matching model to operate in infinite-dimensional spaces. Our approach works by first defining a path of probability…

Machine Learning · Computer Science 2023-12-07 Gavin Kerrigan , Giosue Migliorini , Padhraic Smyth

Flow Matching (FM) is a simulation-free method for learning a continuous and invertible flow to interpolate between two distributions, and in particular to generate data from noise. Inspired by the variational nature of the diffusion…

Machine Learning · Statistics 2025-07-14 Chen Xu , Xiuyuan Cheng , Yao Xie

Flow matching has shown state-of-the-art performance in various generative tasks, ranging from image generation to decision-making, where generation under energy guidance (abbreviated as guidance in the following) is pivotal. However, the…

Machine Learning · Computer Science 2025-05-27 Ruiqi Feng , Chenglei Yu , Wenhao Deng , Peiyan Hu , Tailin Wu

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

Flow Matching has emerged as a powerful framework for learning continuous transformations between distributions, enabling high-fidelity generative modeling. This work introduces Symmetrical Flow Matching (SymmFlow), a new formulation that…

Computer Vision and Pattern Recognition · Computer Science 2026-03-24 Francisco Caetano , Christiaan Viviers , Peter H. N. De With , Fons van der Sommen

Flow matching is a recent framework to train generative models that exhibits impressive empirical performance while being relatively easier to train compared with diffusion-based models. Despite its advantageous properties, prior methods…

Computer Vision and Pattern Recognition · Computer Science 2023-07-18 Quan Dao , Hao Phung , Binh Nguyen , Anh Tran

Over the past decade, advances in generative modeling, such as generative adversarial networks, masked autoencoders, and diffusion models, have significantly transformed biological research and discovery, enabling breakthroughs in molecule…

Machine Learning · Computer Science 2026-03-10 Zihao Li , Zhichen Zeng , Xiao Lin , Feihao Fang , Yanru Qu , Zhe Xu , Zhining Liu , Xuying Ning , Tianxin Wei , Ge Liu , Hanghang Tong , Jingrui He

Recently, Flow Matching models have pushed the boundaries of high-fidelity data generation across a wide range of domains. It typically employs a single large network to learn the entire generative trajectory from noise to data. Despite…

Computer Vision and Pattern Recognition · Computer Science 2025-10-27 Dogyun Park , Taehoon Lee , Minseok Joo , Hyunwoo J. Kim

Flow matching (FM) is a general framework for defining probability paths via Ordinary Differential Equations (ODEs) to transform between noise and data samples. Recent approaches attempt to straighten these flow trajectories to generate…

Computer Vision and Pattern Recognition · Computer Science 2024-07-03 Ling Yang , Zixiang Zhang , Zhilong Zhang , Xingchao Liu , Minkai Xu , Wentao Zhang , Chenlin Meng , Stefano Ermon , Bin Cui

While generative modeling has achieved remarkable success on tasks like natural language-conditioned image generation, enabling model adaptation from example data points remains a relatively underexplored and challenging problem. To this…

Machine Learning · Computer Science 2026-05-08 Tyler Ingebrand , Ruihan Zhao , Kushagra Gupta , David Fridovich-Keil , Sandeep P. Chinchali , Ufuk Topcu

This paper proposes a novel method, Explicit Flow Matching (ExFM), for training and analyzing flow-based generative models. ExFM leverages a theoretically grounded loss function, ExFM loss (a tractable form of Flow Matching (FM) loss), to…

Machine Learning · Computer Science 2024-07-03 Gleb Ryzhakov , Svetlana Pavlova , Egor Sevriugov , Ivan Oseledets

Diffusion and flow-based models have become the state of the art for generative AI across a wide range of data modalities, including images, videos, shapes, molecules, music, and more. This tutorial provides a self-contained introduction to…

Machine Learning · Computer Science 2026-03-19 Peter Holderrieth , Ezra Erives

Flow Matching (FM) is an effective framework for training a model to learn a vector field that transports samples from a source distribution to a target distribution. To train the model, early FM methods use random couplings, which often…

Computer Vision and Pattern Recognition · Computer Science 2025-05-30 Yexiong Lin , Yu Yao , Tongliang Liu

Generative models have shown great promise in collaborative filtering by capturing the underlying distribution of user interests and preferences. However, existing approaches struggle with inaccurate posterior approximations and…

Information Retrieval · Computer Science 2025-09-08 Chengkai Liu , Yangtian Zhang , Jianling Wang , Rex Ying , James Caverlee

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

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 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

Deep learning models have emerged as a powerful tool for various medical applications. However, their success depends on large, high-quality datasets that are challenging to obtain due to privacy concerns and costly annotation. Generative…

Computer Vision and Pattern Recognition · Computer Science 2025-03-04 Milad Yazdani , Yasamin Medghalchi , Pooria Ashrafian , Ilker Hacihaliloglu , Dena Shahriari

Flow matching (FM) is increasingly used in scientific domains for time series generation and forecasting, where data often arise from underlying dynamical systems. However, it is not well-understood whether it learns transferable dynamical…

Machine Learning · Statistics 2026-05-08 Soon Hoe Lim , Shizheng Lin , Michael W. Mahoney , N. Benjamin Erichson
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