  Generative adversarial networks (GANs) are one of the most popular approaches
when it comes to training generative models, among which variants of
Wasserstein GANs are considered superior to the standard GAN formulation in
terms of learning stability and sample quality. However, Wasserstein GANs
require the critic to be 1-Lipschitz, which is often enforced implicitly by
penalizing the norm of its gradient, or by globally restricting its Lipschitz
constant via weight normalization techniques. Training with a regularization
term penalizing the violation of the Lipschitz constraint explicitly, instead
of through the norm of the gradient, was found to be practically infeasible in
most situations. Inspired by Virtual Adversarial Training, we propose a method
called Adversarial Lipschitz Regularization, and show that using an explicit
Lipschitz penalty is indeed viable and leads to competitive performance when
applied to Wasserstein GANs, highlighting an important connection between
Lipschitz regularization and adversarial training.
