  We introduce a new method for training generative adversarial networks by
applying the Wasserstein-2 metric proximal on the generators. The approach is
based on Wasserstein information geometry. It defines a parametrization
invariant natural gradient by pulling back optimal transport structures from
probability space to parameter space. We obtain easy-to-implement iterative
regularizers for the parameter updates of implicit deep generative models. Our
experiments demonstrate that this method improves the speed and stability of
training in terms of wall-clock time and Fr\'echet Inception Distance.
