# DPOT: A DeepParticle method for Computation of Optimal Transport with convergence guarantee

arXiv: https://arxiv.org/abs/2506.23429 · HTML: https://mlsanity.com/paper/2506.23429/

## Key facts

- Cited by 1 papers in the map (data through 14 Oct 2026).
- Builds on 21 of its 45 references that are in the map.
- First posted on arXiv 29 Jun 2025.

## Builds on (most cited first, 21 of 21)

- [Deep Residual Learning for Image Recognition](https://mlsanity.com/paper/1512.03385/) (2015)
- [Sinkhorn Distances: Lightspeed Computation of Optimal Transportation Distances](https://mlsanity.com/paper/1306.0895/) (2013)
- [Diffusion Schr"odinger Bridge with Applications to Score-Based Generative Modeling](https://mlsanity.com/paper/2106.01357/) (2021)
- [The Deep Ritz method: A deep learning-based numerical algorithm for solving variational problems](https://mlsanity.com/paper/1710.00211/) (2017)
- [Optimal transport mapping via input convex neural networks](https://mlsanity.com/paper/1908.10962/) (2019)
- [Large-Scale Optimal Transport and Mapping Estimation](https://mlsanity.com/paper/1711.02283/) (2017)
- [Wasserstein-2 Generative Networks](https://mlsanity.com/paper/1909.13082/) (2019)
- [Generative Modeling with Optimal Transport Maps](https://mlsanity.com/paper/2110.02999/) (2021)
- [Score-based Generative Neural Networks for Large-Scale Optimal Transport](https://mlsanity.com/paper/2110.03237/) (2021)
- [Optimal Transport for Offline Imitation Learning](https://mlsanity.com/paper/2303.13971/) (2023)
- [Neural Monge Map estimation and its applications](https://mlsanity.com/paper/2106.03812/) (2021)
- [On the Efficiency of Entropic Regularized Algorithms for Optimal Transport](https://mlsanity.com/paper/1906.01437/) (2019)
- [Energy-guided Entropic Neural Optimal Transport](https://mlsanity.com/paper/2304.06094/) (2023)
- [Global Adaptation meets Local Generalization: Unsupervised Domain Adaptation for 3D Human Pose Estimation](https://mlsanity.com/paper/2303.16456/) (2023)
- [On a Combination of Alternating Minimization and Nesterov's Momentum](https://mlsanity.com/paper/1906.03622/) (2019)
- [DeepParticle: learning invariant measure by a deep neural network minimizing Wasserstein distance on data generated from an interacting particle method](https://mlsanity.com/paper/2111.01356/) (2021)
- [Mode Collapse and Regularity of Optimal Transportation Maps](https://mlsanity.com/paper/1902.02934/) (2019)
- [Anomaly detection with Wasserstein GAN](https://mlsanity.com/paper/1812.02463/) (2018)
- [Randomized methods for computing optimal transport without regularization and their convergence analysis](https://mlsanity.com/paper/2212.07046/) (2022)
- [A DeepParticle method for learning and generating aggregation patterns in multi-dimensional Keller-Segel chemotaxis systems](https://mlsanity.com/paper/2209.00109/) (2022)
- [Self-reinforced polynomial approximation methods for concentrated probability densities](https://mlsanity.com/paper/2303.02554/) (2023)

## Built on by (most cited first, 1 of 1)

- [COFM: Consistent Optimal Transport Flow Matching via Partially Input Convex Neural Networks](https://mlsanity.com/paper/2511.06042/) (2025)

## Abstract (arXiv)

In this work, we propose a novel machine learning approach to compute the optimal transport map between two continuous distributions from their unpaired samples, based on the DeepParticle methods. The proposed method leads to a min-min optimization during training and does not impose any restriction on the network structure. Theoretically we establish a weak convergence guarantee and a quantitative error bound between the learned map and the optimal transport map. Our numerical experiments validate the theoretical results and the effectiveness of the new approach, particularly on real-world tasks.