# Large-Scale Optimal Transport via Adversarial Training with Cycle-Consistency

arXiv: https://arxiv.org/abs/2003.06635 · HTML: https://mlsanity.com/paper/2003.06635/

## Key facts

- Cited by 14 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 14 Mar 2020.

## Built on by (most cited first, 14 of 14)

- [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)
- [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)
- [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)
- [An Optimal Transport Perspective on Unpaired Image Super-Resolution](https://mlsanity.com/paper/2202.01116/) (2022)
- [Neural Wasserstein Gradient Flows for Maximum Mean Discrepancies with Riesz Kernels](https://mlsanity.com/paper/2301.11624/) (2023)
- [Neural Hamilton--Jacobi Characteristic Flows for Optimal Transport](https://mlsanity.com/paper/2510.01153/) (2025)
- [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)

Recent advances in large-scale optimal transport have greatly extended its application scenarios in machine learning. However, existing methods either not explicitly learn the transport map or do not support general cost function. In this paper, we propose an end-to-end approach for large-scale optimal transport, which directly solves the transport map and is compatible with general cost function. It models the transport map via stochastic neural networks and enforces the constraint on the marginal distributions via adversarial training. The proposed framework can be further extended towards learning Monge map or optimal bijection via adopting cycle-consistency constraint(s). We verify the effectiveness of the proposed method and demonstrate its superior performance against existing methods with large-scale real-world applications, including domain adaptation, image-to-image translation, and color transfer.