We introduce a new method for training GANs by applying the Wasserstein-2 metric proximal on the generators. 
 The approach is based on the gradient operator induced by optimal transport, which connects the geometry of sample space and parameter space in implicit deep generative models. From this theory, we obtain an easy-to-implement regularizer for the parameter updates. Our experiments demonstrate that this method improves the speed and stability in training GANs in terms of wall-clock time and Fr\'echet Inception Distance (FID) learning curves.
We propose the Wasserstein proximal method for training GANs.  Proposes a new GAN procedure that takes into account points generated in the previous iteration and updates the generator to be carried out l times. Considers natural gradient learning in GAN learning, where the Riemannian structure induced by the Wasserstein-2 distance is employed. The paper intends to utilize natural gradient induced by Wasserstein-2 distance to train the generator in GAN and the authors propose the Wasserstein proximal operator as a regularization.