Extremal Domain Translation with Neural Optimal Transport

TL;DR

This paper introduces extremal transport, a mathematical framework for optimal unpaired image translation that aims to produce the most similar translated images to their inputs, leveraging neural optimal transport techniques.

Contribution

It formalizes extremal transport as the best possible unpaired translation and proposes a scalable neural algorithm to approximate it.

Findings

Effective on toy examples

Successful application to image-to-image translation

Code implementation available online

Abstract

In many unpaired image domain translation problems, e.g., style transfer or super-resolution, it is important to keep the translated image similar to its respective input image. We propose the extremal transport (ET) which is a mathematical formalization of the theoretically best possible unpaired translation between a pair of domains w.r.t. the given similarity function. Inspired by the recent advances in neural optimal transport (OT), we propose a scalable algorithm to approximate ET maps as a limit of partial OT maps. We test our algorithm on toy examples and on the unpaired image-to-image translation task. The code is publicly available at https://github.com/milenagazdieva/ExtremalNeuralOptimalTransport