Optimal Transport (OT) problem aims to find a transport plan that bridges two distributions while minimizing a given cost function. OT theory has been widely utilized in generative modeling. In the beginning, OT distance has been used as a measure for assessing the distance between data and generated distributions. Recently, OT transport map between data and prior distributions has been utilized as a generative model. These OT-based generative models share a similar adversarial training objective. In this paper, we begin by unifying these OT-based adversarial methods within a single framework. Then, we elucidate the role of each component in training dynamics through a comprehensive analysis of this unified framework. Moreover, we suggest a simple but novel method that improves the previously best-performing OT-based model. Intuitively, our approach conducts a gradual refinement of the generated distribution, progressively aligning it with the data distribution. Our approach achieves a FID score of 2.51 on CIFAR-10 and 5.99 on CelebA-HQ-256, outperforming unified OT-based adversarial approaches.

翻译：最优传输（Optimal Transport, OT）问题旨在寻找一个连接两个分布且最小化给定成本函数的传输方案。OT理论已广泛应用于生成建模领域。最初，OT距离被用作评估数据分布与生成分布之间距离的度量。近年来，数据分布与先验分布之间的OT传输映射被用作生成模型。这些基于OT的生成模型共享相似的对抗训练目标。本文首先将这些基于OT的对抗方法统一纳入一个框架中。随后，通过对该统一框架的全面分析，我们阐明了各组件在训练动态中的作用。此外，我们提出了一种简单而新颖的方法，改进了先前性能最佳的OT模型。直观上，我们的方法对生成分布进行逐步细化，使其渐进地与数据分布对齐。该方法在CIFAR-10上取得了2.51的FID分数，在CelebA-HQ-256上取得了5.99的FID分数，优于统一的OT对抗方法。