Papers › Adversarial Computation of Optimal Transport Maps

Adversarial Computation of Optimal Transport Maps

24 Jun 2019arXiv:1906.09691archive 2025-07-28

Jacob Leygonie, Jennifer She, Amjad Almahairi, Sai Rajeswar, Aaron Courville

Computing optimal transport maps between high-dimensional and continuous distributions is a challenging problem in optimal transport (OT). Generative adversarial networks (GANs) are powerful generative models which have been successfully applied to learn maps across high-dimensional domains. However, little is known about the nature of the map learned with a GAN objective. To address this problem, we propose a generative adversarial model in which the discriminator's objective is the 2-Wasserstein metric. We show that during training, our generator follows the W₂-geodesic between the initial and the target distributions. As a consequence, it reproduces an optimal map at the end of training. We validate our approach empirically in both low-dimensional and high-dimensional continuous settings, and show that it outperforms prior methods on image data.

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