# Extremal Domain Translation with Neural Optimal Transport

arXiv: https://arxiv.org/abs/2301.12874 · HTML: https://mlsanity.com/paper/2301.12874/

## Key facts

- Cited by 12 papers in the map (data through 14 Oct 2026).
- Builds on 47 of its 78 references that are in the map.
- First posted on arXiv 30 Jan 2023.

## Builds on (most cited first, 30 of 47)

- [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)
- [Learning Transferable Visual Models From Natural Language Supervision](https://mlsanity.com/paper/2103.00020/) (2021)
- [Language Models are Few-Shot Learners](https://mlsanity.com/paper/2005.14165/) (2020)
- [U-Net: Convolutional Networks for Biomedical Image Segmentation](https://mlsanity.com/paper/1505.04597/) (2015)
- [The Unreasonable Effectiveness of Deep Features as a Perceptual Metric](https://mlsanity.com/paper/1801.03924/) (2018)
- [Hierarchical Text-Conditional Image Generation with CLIP Latents](https://mlsanity.com/paper/2204.06125/) (2022)
- [A Style-Based Generator Architecture for Generative Adversarial Networks](https://mlsanity.com/paper/1812.04948/) (2018)
- [Deep Learning Face Attributes in the Wild](https://mlsanity.com/paper/1411.7766/) (2014)
- [Billion-scale similarity search with GPUs](https://mlsanity.com/paper/1702.08734/) (2017)
- [Improved Training of Wasserstein GANs](https://mlsanity.com/paper/1704.00028/) (2017)
- [Describing Textures in the Wild](https://mlsanity.com/paper/1311.3618/) (2013)
- [LSUN: Construction of a Large-scale Image Dataset using Deep Learning with Humans in the Loop](https://mlsanity.com/paper/1506.03365/) (2015)
- [Demystifying MMD GANs](https://mlsanity.com/paper/1801.01401/) (2018)
- [StarGAN v2: Diverse Image Synthesis for Multiple Domains](https://mlsanity.com/paper/1912.01865/) (2019)
- [Efficient and robust approximate nearest neighbor search using Hierarchical Navigable Small World graphs](https://mlsanity.com/paper/1603.09320/) (2016)
- [Multimodal Unsupervised Image-to-Image Translation](https://mlsanity.com/paper/1804.04732/) (2018)
- [Computational Optimal Transport](https://mlsanity.com/paper/1803.00567/) (2018)
- [Wasserstein GAN](https://mlsanity.com/paper/1701.07875/) (2017)
- [Learning Generative Models with Sinkhorn Divergences](https://mlsanity.com/paper/1706.00292/) (2017)
- [Are GANs Created Equal? A Large-Scale Study](https://mlsanity.com/paper/1711.10337/) (2017)
- [Optimal transport mapping via input convex neural networks](https://mlsanity.com/paper/1908.10962/) (2019)
- [Neural Style Transfer: A Review](https://mlsanity.com/paper/1705.04058/) (2017)
- [Stochastic Optimization for Large-scale Optimal Transport](https://mlsanity.com/paper/1605.08527/) (2016)
- [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)
- [Large-Scale Optimal Transport and Mapping Estimation](https://mlsanity.com/paper/1711.02283/) (2017)
- [Image-to-Image Translation: Methods and Applications](https://mlsanity.com/paper/2101.08629/) (2021)
- [Wasserstein-2 Generative Networks](https://mlsanity.com/paper/1909.13082/) (2019)
- [Do Neural Optimal Transport Solvers Work? A Continuous Wasserstein-2 Benchmark](https://mlsanity.com/paper/2106.01954/) (2021)

## Built on by (most cited first, 12 of 12)

- [Optimal Flow Matching: Learning Straight Trajectories in Just One Step](https://mlsanity.com/paper/2403.13117/) (2024)
- [Light Schr"odinger Bridge](https://mlsanity.com/paper/2310.01174/) (2023)
- [Energy-Guided Continuous Entropic Barycenter Estimation for General Costs](https://mlsanity.com/paper/2310.01105/) (2023)
- [Robust Barycenter Estimation using Semi-Unbalanced Neural Optimal Transport](https://mlsanity.com/paper/2410.03974/) (2024)
- [Rethinking Optimal Transport in Offline Reinforcement Learning](https://mlsanity.com/paper/2410.14069/) (2024)
- [Learning of Population Dynamics: Inverse Optimization Meets JKO Scheme](https://mlsanity.com/paper/2506.01502/) (2025)
- [Light Unbalanced Optimal Transport](https://mlsanity.com/paper/2303.07988/) (2023)
- [ENOT: Expectile Regularization for Fast and Accurate Training of Neural Optimal Transport](https://mlsanity.com/paper/2403.03777/) (2024)
- [Optimal Transport Maps are Good Voice Converters](https://mlsanity.com/paper/2411.02402/) (2024)
- [A Statistical Learning Perspective on Semi-dual Adversarial Neural Optimal Transport Solvers](https://mlsanity.com/paper/2502.01310/) (2025)
- [Rethinking the Flow-Based Gradual Domain Adaptation: A Semi-Dual Optimal Transport Perspective](https://mlsanity.com/paper/2602.01179/) (2026)
- [Simultaneous Neural Optimal Transport](https://mlsanity.com/paper/2609.37424/) (2026)

## Abstract (arXiv)

In many unpaired image domain translation problems, e.g., style transfer or super-resolution, it is important to keep the translated image similar to its respective input image. We propose the extremal transport (ET) which is a mathematical formalization of the theoretically best possible unpaired translation between a pair of domains w.r.t. the given similarity function. Inspired by the recent advances in neural optimal transport (OT), we propose a scalable algorithm to approximate ET maps as a limit of partial OT maps. We test our algorithm on toy examples and on the unpaired image-to-image translation task. The code is publicly available at https://github.com/milenagazdieva/ExtremalNeuralOptimalTransport