Wasserstein-2 Generative Networks
Authors: Alexander Korotin, Vage Egiazarian, Arip Asadulaev, Alexander Safin, Evgeny Burnaev
Venue: ICLR 2021 Poster
Keywords: wasserstein-2 distance, optimal transport maps, non-minimax optimization, cycle-consistency regularization, input-convex neural networks
Abstract: We propose a novel end-to-end non-minimax algorithm for training optimal transport mappings for the quadratic cost (Wasserstein-2 distance). The algorithm uses input convex neural networks and a cycle-consistency regularization to approximate Wasserstein-2 distance. In contrast to popular entropic and quadratic regularizers, cycle-consistency does not introduce bias and scales well to high dimensions. From the theoretical side, we estimate the properties of the generative mapping fitted by our algorithm. From the practical side, we evaluate our algorithm on a wide range of tasks: image-to-image color transfer, latent space optimal transport, image-to-image style transfer, and domain adaptation.