Wasserstein GAN with Quadratic Transport Cost

Wasserstein GANs are increasingly used in Computer Vision applications as they are easier to train. Previous WGAN variants mainly use the l(1) transport cost to compute the Wasserstein distance between the real and synthetic data distributions. The l(1) transport cost restricts the discriminator to be 1-Lipschitz. However, WGANs with l(1) transport cost were recently shown to not always converge. In this paper, we propose WGAN-QC, a WGAN with quadratic transport cost. Based on the quadratic transport cost, we propose an Optimal Transport Regularizer (OTR) to stabilize the training process of WGAN-QC. We prove that the objective of the discriminator during each generator update computes the exact quadratic Wasserstein distance between real and synthetic data distributions. We also prove that WGAN-QC converges to a local equilibrium point with finite discriminator updates per generator update. We show experimentally on a Dirac distribution that WGAN-QC converges, when many of the l(1) cost WGANs fail to [22]. Qualitative and quantitative results on the CelebA, CelebA-HQ, LSUN and the ImageNet dog datasets show that WGAN-QC is better than state-of-art GAN methods. WGAN-QC has much faster runtime than other WGAN variants.