# OT-Net: A Reusable Neural Optimal Transport Solver

arXiv: https://arxiv.org/abs/2306.08233 · HTML: https://mlsanity.com/paper/2306.08233/

## Key facts

- Cited by 2 papers in the map (data through 14 Oct 2026).
- Builds on 43 of its 75 references that are in the map.
- First posted on arXiv 14 Jun 2023.

## Builds on (most cited first, 30 of 43)

- [Adam: A Method for Stochastic Optimization](https://mlsanity.com/paper/1412.6980/) (2014)
- [Fashion-MNIST: a Novel Image Dataset for Benchmarking Machine Learning Algorithms](https://mlsanity.com/paper/1708.07747/) (2017)
- [Improved Techniques for Training GANs](https://mlsanity.com/paper/1606.03498/) (2016)
- [Sinkhorn Distances: Lightspeed Computation of Optimal Transportation Distances](https://mlsanity.com/paper/1306.0895/) (2013)
- [Improved Training of Wasserstein GANs](https://mlsanity.com/paper/1704.00028/) (2017)
- [Least Squares Generative Adversarial Networks](https://mlsanity.com/paper/1611.04076/) (2016)
- [Wasserstein GAN](https://mlsanity.com/paper/1701.07875/) (2017)
- [Optimal Transport for Domain Adaptation](https://mlsanity.com/paper/1507.00504/) (2015)
- [Joint Distribution Optimal Transportation for Domain Adaptation](https://mlsanity.com/paper/1705.08848/) (2017)
- [Are GANs Created Equal? A Large-Scale Study](https://mlsanity.com/paper/1711.10337/) (2017)
- [Adversarially Learned Inference](https://mlsanity.com/paper/1606.00704/) (2016)
- [DeepJDOT: Deep Joint Distribution Optimal Transport for Unsupervised Domain Adaptation](https://mlsanity.com/paper/1803.10081/) (2018)
- [Unrolled Generative Adversarial Networks](https://mlsanity.com/paper/1611.02163/) (2016)
- [Optimal transport mapping via input convex neural networks](https://mlsanity.com/paper/1908.10962/) (2019)
- [VEEGAN: Reducing Mode Collapse in GANs using Implicit Variational Learning](https://mlsanity.com/paper/1705.07761/) (2017)
- [Optimizing the Latent Space of Generative Networks](https://mlsanity.com/paper/1707.05776/) (2017)
- [Neural Optimal Transport](https://mlsanity.com/paper/2201.12220/) (2022)
- [Large-Scale Optimal Transport and Mapping Estimation](https://mlsanity.com/paper/1711.02283/) (2017)
- [BEGAN: Boundary Equilibrium Generative Adversarial Networks](https://mlsanity.com/paper/1703.10717/) (2017)
- [Computational Optimal Transport: Complexity by Accelerated Gradient Descent Is Better Than by Sinkhorn's Algorithm](https://mlsanity.com/paper/1802.04367/) (2018)
- [PacGAN: The power of two samples in generative adversarial networks](https://mlsanity.com/paper/1712.04086/) (2017)
- [Generative Modeling with Optimal Transport Maps](https://mlsanity.com/paper/2110.02999/) (2021)
- [On the regularization of Wasserstein GANs](https://mlsanity.com/paper/1709.08894/) (2017)
- [Score-based Generative Neural Networks for Large-Scale Optimal Transport](https://mlsanity.com/paper/2110.03237/) (2021)
- [Unified Optimal Transport Framework for Universal Domain Adaptation](https://mlsanity.com/paper/2210.17067/) (2022)
- [From Facial Expression Recognition to Interpersonal Relation Prediction](https://mlsanity.com/paper/1609.06426/) (2016)
- [Variational Approaches for Auto-Encoding Generative Adversarial Networks](https://mlsanity.com/paper/1706.04987/) (2017)
- [On the Convergence and Robustness of Training GANs with Regularized Optimal Transport](https://mlsanity.com/paper/1802.08249/) (2018)
- [Many Paths to Equilibrium: GANs Do Not Need to Decrease a Divergence At Every Step](https://mlsanity.com/paper/1710.08446/) (2017)
- [Geometric Understanding of Deep Learning](https://mlsanity.com/paper/1805.10451/) (2018)

## Built on by (most cited first, 2 of 2)

- [NoPain: No-box Point Cloud Attack via Optimal Transport Singular Boundary](https://mlsanity.com/paper/2503.00063/) (2025)
- [HOTS3D: Hyper-Spherical Optimal Transport for Semantic Alignment of Text-to-3D Generation](https://mlsanity.com/paper/2407.14419/) (2024)

## Abstract (arXiv)

With the widespread application of optimal transport (OT), its calculation becomes essential, and various algorithms have emerged. However, the existing methods either have low efficiency or cannot represent discontinuous maps. A novel reusable neural OT solver OT-Net is thus presented, which first learns Brenier's height representation via the neural network to obtain its potential, and then gained the OT map by computing the gradient of the potential. The algorithm has two merits, 1) it can easily represent discontinuous maps, which allows it to match any target distribution with discontinuous supports and achieve sharp boundaries. This can well eliminate mode collapse in the generated models. 2) The OT map can be calculated straightly by the proposed algorithm when new target samples are added, which greatly improves the efficiency and reusability of the map. Moreover, the theoretical error bound of the algorithm is analyzed, and we have demonstrated the empirical success of our approach in image generation, color transfer, and domain adaptation.