A Theory on Flow Matching with Neural Networks

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.

Machine Learning (cs.LG); Artificial Intelligence (cs.AI)

arXiv:2606.10089 [cs.LG]

(or arXiv:2606.10089v1 [cs.LG] for this version)

https://doi.org/10.48550/arXiv.2606.10089 Focus to learn more arXiv-issued DOI via DataCite

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