With the widespread application of optimal transport (OT), its calculation
becomes essential, and various algorithms have emerged. However, the existing
methods either have low efficiency or cannot represent discontinuous maps. A
novel reusable neural OT solver OT-Net is thus presented, which first learns
Brenier's height representation via the neural network to obtain its potential,
and then gained the OT map by computing the gradient of the potential. The
algorithm has two merits, 1) it can easily represent discontinuous maps, which
allows it to match any target distribution with discontinuous supports and
achieve sharp boundaries. This can well eliminate mode collapse in the
generated models. 2) The OT map can be calculated straightly by the proposed
algorithm when new target samples are added, which greatly improves the
efficiency and reusability of the map. Moreover, the theoretical error bound of
the algorithm is analyzed, and we have demonstrated the empirical success of
our approach in image generation, color transfer, and domain adaptation.

提出了一种使用神经网络进行最优传输计算的算法 OT-Net，可以表示不连续映射，在图像生成、颜色转移、域适应等方面取得了良好的应用效果。