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Recent advances in large-scale optimal transport have greatly extended itsapplication scenarios in machine learning. However, existing methods either notexplicitly learn the transport map or do not support general cost function. Inthis paper, we propose an end-to-end approach for large-scale optimaltransport, which directly solves the transport map and is compatible withgeneral cost function. It models the transport map via stochastic neuralnetworks and enforces the constraint on the marginal distributions viaadversarial training. The proposed framework can be further extended towardslearning Monge map or optimal bijection via adopting cycle-consistencyconstraint(s). We verify the effectiveness of the proposed method anddemonstrate its superior performance against existing methods with large-scalereal-world applications, including domain adaptation, image-to-imagetranslation, and color transfer.

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