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 5.80 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）问题研究在最小化给定代价函数的同时，连接两个分布的传输映射。在此方面，可处理先验分布与数据之间的OT已被用于生成建模任务。然而，基于OT的方法易受异常值影响，并在训练过程中面临优化挑战。本文提出了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OT不同，UOT放宽了对分布匹配的硬约束。该方法对异常值具有更好的鲁棒性，训练过程中更稳定，且收敛速度更快。我们通过实验验证了这些性质。此外，我们研究了UOT中分布间散度的理论上界。我们的模型优于现有的基于OT的生成模型，在CIFAR-10上实现了2.97的FID分数，在CelebA-HQ-256上实现了5.80的FID分数。代码可在\url{https://github.com/Jae-Moo/UOTM}获取。