Potential Flow Generator With L2 Optimal Transport Regularity for Generative Models

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 generative adversarial networks (GANs) and normalizing flow models. With only a slight augmentation to the original generator loss functions, our generator not only tries to transport the input distribution to the target one but also aims to find the one with minimum $L_{2}$ transport cost. We show the effectiveness of our method in several 2-D 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 data set and the CelebA data set with a comparison against vanilla Wasserstein GAN with gradient penalty (WGAN-GP) and CycleGAN.