Optimal Transport (OT) theory investigates the cost-minimizing transport map that moves a source distribution to a target distribution. Recently, several approaches have emerged for learning the optimal transport map for a given cost function using neural networks. We refer to these approaches as the OT Map. OT Map provides a powerful tool for diverse machine learning tasks, such as generative modeling and unpaired image-to-image translation. However, existing methods that utilize max-min optimization often experience training instability and sensitivity to hyperparameters. In this paper, we propose a novel method to improve stability and achieve a better approximation of the OT Map by exploiting displacement interpolation, dubbed Displacement Interpolation Optimal Transport Model (DIOTM). We derive the dual formulation of displacement interpolation at specific time $t$ and prove how these dual problems are related across time. This result allows us to utilize the entire trajectory of displacement interpolation in learning the OT Map. Our method improves the training stability and achieves superior results in estimating optimal transport maps. We demonstrate that DIOTM outperforms existing OT-based models on image-to-image translation tasks.

本研究解决了现有最优传输方法在训练不稳定性和超参数敏感性方面的不足。提出了一种新颖的位移插值最优传输模型（DIOTM），通过利用位移插值的整个轨迹，显著改善了训练稳定性，并在图像到图像的翻译任务中超越了现有的最优传输模型。该方法展示了在估计最优传输地图方面的优越性能和潜在影响。

通过位移插值改进神经最优传输