[4S2-GS-2] Machine learning:

[4S2-GS-2-02] Minimizing Wasserstein Distance by Discriminator for Flow Matching

〇Daiki Miyake¹, Masahiro Suzuki¹, Yutaka Matsuo¹ (1. The University of Tokyo)

Keywords:Flow Matching, Diffusion Models, Wasserstein distance

In training deep generative models, it is essential how to approach the generated distribution to the data distribution. The most used measure is KL divergence, however, it has the problem that the gradent based optimization is difficult when the two distributions do not have any intersections. Flow matching is a deep generative model whose application has been widely studied, it can be regarded as minimizing the upper bound of KL divergence as diffusion models do. Then, we propose a method to minimize Wasserstein distance in flow matching formulation. We introduce a discriminator to calculate Wasserstein distance, and approach the time derivative of the distance to 0. In 2d dataset experiments, we verify that the proposed method minimizes Wasserstein distance by training. Although the proposed method would not outperform the original flow matching, we investigate the effect of the discriminator performance by using entropic regularization.