A Theory on Flow Matching with Neural Networks

This paper presents a theoretical framework for flow matching using neural networks, focusing on conditional velocity fields parameterized by 2-layered ReLU networks. It establishes convergence guarantees for gradient descent and derives generalization bounds for the matching objective, along with Wasserstein-distance guarantees for generated samples. These findings are validated through experiments on synthetic and real-world image datasets, providing valuable insights for practitioners in flow-based generative modeling and multi-task representation learning.