Optimal Transport (OT) problem investigates a transport map that bridges two distributions while minimizing a given cost function. In this regard, OT between tractable prior distribution and data has been utilized for generative modeling tasks. However, OT-based methods are susceptible to outliers and face optimization challenges during training. In this paper, we propose a novel generative model based on the semi-dual formulation of Unbalanced Optimal Transport (UOT). Unlike OT, UOT relaxes the hard constraint on distribution matching. This approach provides better robustness against outliers, stability during training, and faster convergence. We validate these properties empirically through experiments. Moreover, we study the theoretical upper-bound of divergence between distributions in UOT. Our model outperforms existing OT-based generative models, achieving FID scores of 2.97 on CIFAR-10 and 6.36 on CelebA-HQ-256. The code is available at \url{https://github.com/Jae-Moo/UOTM}.

翻译：最优传输（Optimal Transport, OT）问题探讨了在最小化给定代价函数的前提下，连接两个分布之间的传输映射。在此背景下，可处理先验分布与数据之间的最优传输已被应用于生成建模任务。然而，基于最优传输的方法对异常值敏感，且在训练过程中面临优化挑战。本文提出一种基于非平衡最优传输（Unbalanced Optimal Transport, UOT）半对偶形式的新型生成模型。与最优传输不同，非平衡最优传输放宽了对分布匹配的严格约束。该方法在应对异常值时具有更强的鲁棒性，训练过程更稳定，且收敛速度更快。我们通过实验实证验证了这些特性。此外，我们研究了非平衡最优传输中分布间散度的理论上界。我们的模型优于现有的基于最优传输的生成模型，在CIFAR-10数据集上实现了2.97的FID分数，在CelebA-HQ-256数据集上实现了6.36的FID分数。代码已公开在 \url{https://github.com/Jae-Moo/UOTM}。