Extremal Domain Translation with Neural Optimal Transport
This work addresses the challenge of preserving input similarity in unpaired translation tasks like style transfer or super-resolution, offering a novel theoretical and computational approach.
The paper tackles the problem of unpaired image domain translation by proposing extremal transport (ET) as a theoretical framework for optimal translation with respect to a similarity function, and develops a scalable neural algorithm to approximate ET maps, testing it on toy examples and image-to-image translation tasks.
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