Potential Flow Generator with $L_2$ Optimal Transport Regularity for Generative Models

Liu Yang, George Em Karniadakis

TL;DR: We propose a special generator with $L_2$ optimal transport regularity, which can be easily integrated into a wide range of generative models.

Abstract: We propose a potential flow generator with $L_2$ optimal transport regularity, which can be easily integrated into a wide range of generative models including different versions of GANs and flow-based models. With up to a slight augmentation of the original generator loss functions, our generator is not only a transport map from the input distribution to the target one, but also the one with minimum $L_2$ transport cost. We show the correctness and robustness of the potential flow generator in several 2D problems, and illustrate the concept of ``proximity'' due to the $L_2$ optimal transport regularity. Subsequently, we demonstrate the effectiveness of the potential flow generator in image translation tasks with unpaired training data from the MNIST dataset and the CelebA dataset.

Code: https://drive.google.com/drive/folders/1I04bvuQqiorxhq4pVedgrmPZKnA6N4-D?usp=sharing

Keywords: generative models, optimal transport, GANs, flow-based models