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This document presents a scalable algorithm for estimating the neural Monge map between two probability distributions, utilizing a weak form of the optimal transport problem that requires only samples from the marginals. The proposed method is capable of handling general cost functions and can be applied to high-dimensional settings without the need for paired data, demonstrating effectiveness in tasks such as text-to-image generation and image inpainting. The algorithm

Author

Yingjian Wang

Language

EN