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arXiv · 2606.10089

A Theory on Flow Matching with Neural Networks

Yihan He·Qishuo Yin·Yuan Cao·Jianqing Fan·Han Liu
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Abstract

In this work, we develop theoretical foundation for flow matching with neural-network-parameterized conditional velocity fields. We establish convergence guarantees for gradient descent in the over-parameterized 2-layered ReLU neural network regime. We derive generalization bounds for the conditional velocity-field matching objective. Building on these results, we provide Wasserstein-distance guarantees for the samples generated by the induced flow. Our analysis is based on generalization bound for multi-task representation learning with unbounded losses, which may be of independent interest beyond flow-based generative modeling. These theoretical results are validated through extensive experiments on both synthetic and real-world image benchmarks.

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Yihan He, Qishuo Yin, Yuan Cao, Jianqing Fan, Han Liu. 2026-06-08. A Theory on Flow Matching with Neural Networks. https://arxiv.org/abs/2606.10089

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