A Theory on Flow Matching with Neural Networks
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Computer Science > Machine Learning
Title: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.
| Subjects: | Machine Learning (cs.LG); Artificial Intelligence (cs.AI) |
| Cite as: | arXiv:2606.10089 [cs.LG] |
| (or arXiv:2606.10089v1 [cs.LG] for this version) | |
| https://doi.org/10.48550/arXiv.2606.10089
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