Guiding the One-to-one Mapping in CycleGAN via Optimal Transport

TL;DR

This paper addresses the lack of theoretical guarantees in CycleGAN's one-to-one mappings by introducing optimal transport constraints to control and improve the learned mappings for specific tasks.

Contribution

The paper proposes a novel method combining optimal transport with CycleGAN to enforce controllable and task-specific one-to-one mappings.

Findings

The proposed method effectively learns mappings with desired properties.

Optimal transport constraints improve the controllability of CycleGAN.

Experimental results demonstrate the method's ability to produce task-aligned mappings.

Abstract

CycleGAN is capable of learning a one-to-one mapping between two data distributions without paired examples, achieving the task of unsupervised data translation. However, there is no theoretical guarantee on the property of the learned one-to-one mapping in CycleGAN. In this paper, we experimentally find that, under some circumstances, the one-to-one mapping learned by CycleGAN is just a random one within the large feasible solution space. Based on this observation, we explore to add extra constraints such that the one-to-one mapping is controllable and satisfies more properties related to specific tasks. We propose to solve an optimal transport mapping restrained by a task-specific cost function that reflects the desired properties, and use the barycenters of optimal transport mapping to serve as references for CycleGAN. Our experiments indicate that the proposed algorithm is capable of learning a one-to-one mapping with the desired properties.