  Joint distribution matching (JDM) problem, which aims to learn bidirectional
mappings to match joint distributions of two domains, occurs in many machine
learning and computer vision applications. This problem, however, is very
difficult due to two critical challenges: (i) it is often difficult to exploit
sufficient information from the joint distribution to conduct the matching;
(ii) this problem is hard to formulate and optimize. In this paper, relying on
optimal transport theory, we propose to address JDM problem by minimizing the
Wasserstein distance of the joint distributions in two domains. However, the
resultant optimization problem is still intractable. We then propose an
important theorem to reduce the intractable problem into a simple optimization
problem, and develop a novel method (called Joint Wasserstein Distribution
Matching (JWDM)) to solve it. In the experiments, we apply our method to
unsupervised image translation and cross-domain video synthesis. Both
qualitative and quantitative comparisons demonstrate the superior performance
of our method over several state-of-the-arts.
