MiS Preprint Repository

We have decided to discontinue the publication of preprints on our preprint server as of 1 March 2024. The publication culture within mathematics has changed so much due to the rise of repositories such as ArXiV ( that we are encouraging all institute members to make their preprints available there. An institute's repository in its previous form is, therefore, unnecessary. The preprints published to date will remain available here, but we will not add any new preprints here.

MiS Preprint

Wasserstein Proximal of GANs

Alex Tong Lin, Wuchen Li, Stanley Osher and Guido Montúfar


We introduce a new method for training GANs by applying the Wasserstein-2 metric proximal on the generators. This approach is based on the gradient operator induced by optimal transport theory, which connects the geometry of the sample space and the 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 wallclock time and Frechet Inception Distance (FID) learning curves.

optimal transport, natural gradient, Generative Adversarial Network

Related publications

2021 Repository Open Access
Alex Tong Lin, Wuchen Li, Stanley Osher and Guido Montúfar

Wasserstein proximal of GANs

In: Geometric science of information : 5th international conference, GSI 2021, Paris, France, July 21-23, 2021, proceedings / Frank Nielsen... (eds.)
Cham : Springer, 2021. - pp. 524-533
(Lecture notes in computer science ; 12829)