# An Optimal Transport Perspective on Unpaired Image Super-Resolution arXiv: https://arxiv.org/abs/2202.01116 ยท HTML: https://mlsanity.com/paper/2202.01116/ ## Key facts - Cited by 12 papers in the map (data through 14 Oct 2026). - Builds on 39 of its 70 references that are in the map. - First posted on arXiv 2 Feb 2022. ## Builds on (most cited first, 30 of 39) - [Deep Residual Learning for Image Recognition](https://mlsanity.com/paper/1512.03385/) (2015) - [Adam: A Method for Stochastic Optimization](https://mlsanity.com/paper/1412.6980/) (2014) - [U-Net: Convolutional Networks for Biomedical Image Segmentation](https://mlsanity.com/paper/1505.04597/) (2015) - [Very Deep Convolutional Networks for Large-Scale Image Recognition](https://mlsanity.com/paper/1409.1556/) (2014) - [The Unreasonable Effectiveness of Deep Features as a Perceptual Metric](https://mlsanity.com/paper/1801.03924/) (2018) - [Rethinking the Inception Architecture for Computer Vision](https://mlsanity.com/paper/1512.00567/) (2015) - [Deep Learning Face Attributes in the Wild](https://mlsanity.com/paper/1411.7766/) (2014) - [Improved Training of Wasserstein GANs](https://mlsanity.com/paper/1704.00028/) (2017) - [Photo-Realistic Single Image Super-Resolution Using a Generative Adversarial Network](https://mlsanity.com/paper/1609.04802/) (2016) - [Enhanced Deep Residual Networks for Single Image Super-Resolution](https://mlsanity.com/paper/1707.02921/) (2017) - [Image Super-Resolution via Iterative Refinement](https://mlsanity.com/paper/2104.07636/) (2021) - [Image Super-Resolution Using Very Deep Residual Channel Attention Networks](https://mlsanity.com/paper/1807.02758/) (2018) - [Multimodal Unsupervised Image-to-Image Translation](https://mlsanity.com/paper/1804.04732/) (2018) - [f-GAN: Training Generative Neural Samplers using Variational Divergence Minimization](https://mlsanity.com/paper/1606.00709/) (2016) - [Towards Principled Methods for Training Generative Adversarial Networks](https://mlsanity.com/paper/1701.04862/) (2017) - [Deep Laplacian Pyramid Networks for Fast and Accurate Super-Resolution](https://mlsanity.com/paper/1704.03915/) (2017) - [Learning from Simulated and Unsupervised Images through Adversarial Training](https://mlsanity.com/paper/1612.07828/) (2016) - [MMD GAN: Towards Deeper Understanding of Moment Matching Network](https://mlsanity.com/paper/1705.08584/) (2017) - [Pros and Cons of GAN Evaluation Measures](https://mlsanity.com/paper/1802.03446/) (2018) - [Unsupervised Image Super-Resolution using Cycle-in-Cycle Generative Adversarial Networks](https://mlsanity.com/paper/1809.00437/) (2018) - [Neural Optimal Transport](https://mlsanity.com/paper/2201.12220/) (2022) - [Unsupervised Cross-Domain Image Generation](https://mlsanity.com/paper/1611.02200/) (2016) - [Frequency Separation for Real-World Super-Resolution](https://mlsanity.com/paper/1911.07850/) (2019) - [Do Neural Optimal Transport Solvers Work? A Continuous Wasserstein-2 Benchmark](https://mlsanity.com/paper/2106.01954/) (2021) - [To learn image super-resolution, use a GAN to learn how to do image degradation first](https://mlsanity.com/paper/1807.11458/) (2018) - [Robust Optimal Transport with Applications in Generative Modeling and Domain Adaptation](https://mlsanity.com/paper/2010.05862/) (2020) - [Unsupervised Real-world Image Super Resolution via Domain-distance Aware Training](https://mlsanity.com/paper/2004.01178/) (2020) - [Generative Modeling with Optimal Transport Maps](https://mlsanity.com/paper/2110.02999/) (2021) - [Understanding SSIM](https://mlsanity.com/paper/2006.13846/) (2020) - [Unpaired Image Super-Resolution using Pseudo-Supervision](https://mlsanity.com/paper/2002.11397/) (2020) ## Built on by (most cited first, 12 of 12) - [The Monge Gap: A Regularizer to Learn All Transport Maps](https://mlsanity.com/paper/2302.04953/) (2023) - [Kernel Neural Optimal Transport](https://mlsanity.com/paper/2205.15269/) (2022) - [Energy-guided Entropic Neural Optimal Transport](https://mlsanity.com/paper/2304.06094/) (2023) - [Estimating Barycenters of Distributions with Neural Optimal Transport](https://mlsanity.com/paper/2402.03828/) (2024) - [Extremal Domain Translation with Neural Optimal Transport](https://mlsanity.com/paper/2301.12874/) (2023) - [Context-Aware Optimal Transport Learning for Retinal Fundus Image Enhancement](https://mlsanity.com/paper/2409.07862/) (2024) - [Light Unbalanced Optimal Transport](https://mlsanity.com/paper/2303.07988/) (2023) - [Data-to-Energy Stochastic Dynamics](https://mlsanity.com/paper/2509.26364/) (2025) - [A Statistical Learning Perspective on Semi-dual Adversarial Neural Optimal Transport Solvers](https://mlsanity.com/paper/2502.01310/) (2025) - [Experts-Guided Unbalanced Optimal Transport for ISP Learning from Unpaired and/or Paired Data](https://mlsanity.com/paper/2512.05635/) (2025) - [Rate-Optimal Noise Annealing in Semi-Dual Neural Optimal Transport: Tangential Identifiability, Off-Manifold Ambiguity, and Guaranteed Recovery](https://mlsanity.com/paper/2602.04110/) (2026) - [Globally Solving Unbalanced Optimal Transport and Density Control for Gaussian Distributions](https://mlsanity.com/paper/2605.04246/) (2026) ## Abstract (arXiv) 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.