🤖 AI Summary
Unpaired image super-resolution (SR) lacks paired low-/high-resolution images, rendering supervised learning inapplicable; while existing GAN-based approaches achieve empirical success, they lack theoretical grounding and rely on complex adversarial training and multiple hand-crafted regularizers. This work establishes, for the first time, a principled connection between GANs and optimal transport (OT): GANs implicitly learn a *biased* OT mapping under unpaired SR. Building on this insight, we propose the first *non-adversarial*, *unbiased* OT-based SR framework, explicitly modeling the unbiased OT map via perceptually weighted Wasserstein distance minimization—eliminating both discriminators and explicit regularizers. We provide theoretical guarantees on convergence and unbiasedness of the solution. Evaluated on the AIM19 unpaired benchmark, our method achieves near-state-of-the-art performance with a significantly simplified objective and markedly improved hyperparameter robustness.
📝 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. 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.
