Multi-marginal Wasserstein GAN

TL;DR

This paper introduces MWGAN, a novel multi-marginal Wasserstein GAN leveraging optimal transport theory to improve multi-domain image translation by effectively measuring and exploiting cross-domain correlations.

Contribution

It proposes a new adversarial objective with domain constraints based on multi-marginal optimal transport, addressing intractability and correlation exploitation challenges.

Findings

MWGAN effectively minimizes Wasserstein distance among multiple domains.

It outperforms existing methods on toy and real-world datasets.

Theoretical analysis confirms its generalization capabilities.

Abstract

Multiple marginal matching problem aims at learning mappings to match a source domain to multiple target domains and it has attracted great attention in many applications, such as multi-domain image translation. However, addressing this problem has two critical challenges: (i) Measuring the multi-marginal distance among different domains is very intractable; (ii) It is very difficult to exploit cross-domain correlations to match the target domain distributions. In this paper, we propose a novel Multi-marginal Wasserstein GAN (MWGAN) to minimize Wasserstein distance among domains. Specifically, with the help of multi-marginal optimal transport theory, we develop a new adversarial objective function with inner- and inter-domain constraints to exploit cross-domain correlations. Moreover, we theoretically analyze the generalization performance of MWGAN, and empirically evaluate it on the balanced and imbalanced translation tasks. Extensive experiments on toy and real-world datasets demonstrate the effectiveness of MWGAN.