为神经网络参数化流匹配提供理论支撑，证明了收敛性与生成样本质量保证。
A Theory on Flow Matching with Neural Networks
- 基于两层ReLU网络，建立梯度下降的收敛性保证
- 推导出条件速度场匹配的泛化界，保障生成样本质量
- 适用于图像生成等任务，对流模型理论有重要价值
本文为神经网络参数化的条件速度场流匹配建立了理论基础。在过参数化的两层ReLU神经网络设置下，我们给出了梯度下降的收敛性保证，并推导了条件速度场匹配目标的泛化界。基于这些结果，我们为生成流诱导的样本提供了Wasserstein距离的保证。分析依赖于具有无界损失的多任务表示学习的泛化界，该结果可能对流模型之外的研究也具独立意义。理论结果在合成数据和真实图像基准上通过大量实验得到验证。
原文摘要 · Abstract (English)
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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