A Theory on Flow Matching with Neural Networks

• URL: http://arxiv.org/abs/2606.10089v1
• Date: Mon, 08 Jun 2026 19:16:32 GMT
• Title: A Theory on Flow Matching with Neural Networks
• Abstract summary: We develop theoretical foundation for flow matching with conditional velocity fields.<n>We derive generalization bounds for the conditional velocity-field matching objective.<n>Our analysis is based on generalization bound for multi-task representation learning with unbounded losses.
• Score: 18.21009159346104
• License: http://creativecommons.org/licenses/by/4.0/
• 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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