  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.
