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. We theoretically investigate optimization problems which arise in such models and find two surprizing 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 propose an algorithm for unpaired SR which learns an unbiased OT map for the perceptual transport cost. Unlike the existing GAN-based alternatives, our algorithm has a simple optimization objective reducing the need for complex hyperparameter selection and an application of additional regularizations. At the same time, it provides a nearly state-of-the-art performance on the large-scale unpaired AIM19 dataset.
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