An Optimal Transport Perspective on Unpaired Image Super-Resolution

Milena Gazdieva (), Petr Mokrov, Litu Rout, Alexander Korotin, Andrey Kravchenko, Alexander Filippov and Evgeny Burnaev
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Milena Gazdieva: Skolkovo Institute of Science and Technology
Petr Mokrov: Skolkovo Institute of Science and Technology
Litu Rout: Indian Space Research Organization
Alexander Korotin: Skolkovo Institute of Science and Technology
Andrey Kravchenko: University of Oxford
Alexander Filippov: AI Foundation and Algorithm Lab
Evgeny Burnaev: Skolkovo Institute of Science and Technology

Journal of Optimization Theory and Applications, 2025, vol. 207, issue 2, No 21, 28 pages

Abstract: 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 behaviour 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. Our source code is publicly available at https://github.com/milenagazdieva/OT-Super-Resolution .

Keywords: Optimal transport; generative modeling; Super-resolution (search for similar items in EconPapers)
Date: 2025
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DOI: 10.1007/s10957-025-02781-7

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