# On Scalable and Efficient Computation of Large Scale Optimal Transport

arXiv: https://arxiv.org/abs/1905.00158 · HTML: https://mlsanity.com/paper/1905.00158/

## Key facts

- Cited by 29 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 1 May 2019.

## Built on by (most cited first, 29 of 29)

- [Neural Optimal Transport](https://mlsanity.com/paper/2201.12220/) (2022)
- [Do Neural Optimal Transport Solvers Work? A Continuous Wasserstein-2 Benchmark](https://mlsanity.com/paper/2106.01954/) (2021)
- [Generative Modeling with Optimal Transport Maps](https://mlsanity.com/paper/2110.02999/) (2021)
- [Continuous Wasserstein-2 Barycenter Estimation without Minimax Optimization](https://mlsanity.com/paper/2102.01752/) (2021)
- [Entropic Neural Optimal Transport via Diffusion Processes](https://mlsanity.com/paper/2211.01156/) (2022)
- [Generative Modeling through the Semi-dual Formulation of Unbalanced Optimal Transport](https://mlsanity.com/paper/2305.14777/) (2023)
- [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)
- [On amortizing convex conjugates for optimal transport](https://mlsanity.com/paper/2210.12153/) (2022)
- [Energy-guided Entropic Neural Optimal Transport](https://mlsanity.com/paper/2304.06094/) (2023)
- [Wasserstein Iterative Networks for Barycenter Estimation](https://mlsanity.com/paper/2201.12245/) (2022)
- [Building the Bridge of Schr"odinger: A Continuous Entropic Optimal Transport Benchmark](https://mlsanity.com/paper/2306.10161/) (2023)
- [An Optimal Transport Perspective on Unpaired Image Super-Resolution](https://mlsanity.com/paper/2202.01116/) (2022)
- [Graph Edit Distance with General Costs Using Neural Set Divergence](https://mlsanity.com/paper/2409.17687/) (2024)
- [Learning High Dimensional Wasserstein Geodesics](https://mlsanity.com/paper/2102.02992/) (2021)
- [Light Unbalanced Optimal Transport](https://mlsanity.com/paper/2303.07988/) (2023)
- [Computing high-dimensional optimal transport by flow neural networks](https://mlsanity.com/paper/2305.11857/) (2023)
- [Analyzing and Improving Optimal-Transport-based Adversarial Networks](https://mlsanity.com/paper/2310.02611/) (2023)
- [Functional optimal transport: map estimation and domain adaptation for functional data](https://mlsanity.com/paper/2102.03895/) (2021)
- [ENOT: Expectile Regularization for Fast and Accurate Training of Neural Optimal Transport](https://mlsanity.com/paper/2403.03777/) (2024)
- [Wasserstein Geodesic Generator for Conditional Distributions](https://mlsanity.com/paper/2308.10145/) (2023)
- [Partial Wasserstein Covering](https://mlsanity.com/paper/2106.00886/) (2021)
- [On Label Shift in Domain Adaptation via Wasserstein Distance](https://mlsanity.com/paper/2110.15520/) (2021)
- [A Class-aware Optimal Transport Approach with Higher-Order Moment Matching for Unsupervised Domain Adaptation](https://mlsanity.com/paper/2401.15952/) (2024)
- [A Statistical Learning Perspective on Semi-dual Adversarial Neural Optimal Transport Solvers](https://mlsanity.com/paper/2502.01310/) (2025)
- [Neural Hamilton--Jacobi Characteristic Flows for Optimal Transport](https://mlsanity.com/paper/2510.01153/) (2025)
- [Efficient Optimal Transport Algorithm by Accelerated Gradient descent](https://mlsanity.com/paper/2104.05802/) (2021)
- [Neural solver for Wasserstein Geodesics and optimal transport dynamics](https://mlsanity.com/paper/2602.22003/) (2026)
- [Implicit Neural Optimal Transport via Fixed-Point Optimization](https://mlsanity.com/paper/2605.10792/) (2026)

## Abstract (arXiv)

Optimal Transport (OT) naturally arises in many machine learning applications, yet the heavy computational burden limits its wide-spread uses. To address the scalability issue, we propose an implicit generative learning-based framework called SPOT (Scalable Push-forward of Optimal Transport). Specifically, we approximate the optimal transport plan by a pushforward of a reference distribution, and cast the optimal transport problem into a minimax problem. We then can solve OT problems efficiently using primal dual stochastic gradient-type algorithms. We also show that we can recover the density of the optimal transport plan using neural ordinary differential equations. Numerical experiments on both synthetic and real datasets illustrate that SPOT is robust and has favorable convergence behavior. SPOT also allows us to efficiently sample from the optimal transport plan, which benefits downstream applications such as domain adaptation.