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.

本文提出基于Unbalanced Optimal Transport(UOT)的半对偶形式构建的新型生成模型，相比于基于OT的方法在处理噪点，稳定性和训练收敛速度等方面表现更优。通过实验验证了该模型的性质，并研究了UOT之间分布差异的理论上界。实验结果显示，该模型在CIFAR-10和CelebA-HQ-256数据集上的FID分别为2.97和5.80，优于现有基于OT的生成模型。

非平衡最优输运半对偶形式生成建模