An Optimal Transport Perspective on Unpaired Image Super-Resolution

Milena Gazdieva, Petr Mokrov, Litu Rout, Alexander Korotin, Alexander Filippov, Evgeny Burnaev

Keywords: optimal transport, super-resolution, generative modeling, adversarial learning

Abstract: Real-world image super-resolution (SR) tasks often do not have paired datasets, which limits the application of supervised techniques. As a result, the tasks are usually approached by *unpaired* techniques based on Generative Adversarial Networks (GANs), which yield complex training losses with several regularization terms, e.g., content or identity losses. While GANs usually provide good practical performance, they are used heuristically, i.e., theoretical understanding of their behavior is yet rather limited. We theoretically investigate optimization problems which arise in such models and find two surprising observations. First, the learned SR map is always an *optimal transport* (OT) map. Second, we theoretically prove and empirically show that the learned map is *biased*, i.e., it does not actually transform the distribution of low-resolution images to high-resolution ones. Inspired by these findings, we investigate recent advances in neural OT field to resolve the *bias* issue. We establish an intriguing connection between regularized GANs and neural OT approaches. We show that unlike the existing GAN-based alternatives, these algorithms aim to learn an *unbiased* OT map. We empirically demonstrate our findings via a series of synthetic and real-world unpaired SR experiments.

Submission Number: 51