CycleGAN Through the Lens of (Dynamical) Optimal Transport.

Unsupervised Domain Translation (UDT) is the problem of finding a meaningful correspondence between two given domains, without explicit pairings between elements of the domains. Following the seminal CycleGAN model, variants and extensions have been used successfully for a wide range of applications. However, although there have been some attempts, they remain poorly understood, and lack theoretical guarantees. In this work, we explore the implicit biases present in current approaches and demonstrate where and why they fail. By expliciting these biases, we show that UDT can be reframed as an Optimal Transport (OT) problem. Using the dynamical formulation of Optimal Transport, this allows us to improve the CycleGAN model into a simple and practical formulation which comes with theoretical guarantees and added robustness. Finally, we show how our improved model behaves on the CelebA dataset in a standard then in a more challenging setting, thus paving the way for new applications of UDT. Supplementary material is available at https://arxiv.org/pdf/1906.01292.