  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.
