Generative Modeling through the Semi-dual Formulation of Unbalanced Optimal Transport

Jaemoo Choi, Jaewoong Choi, Myungjoo Kang

Keywords: Optimal Transport, Generative modeling, Generative adversarial network

TL;DR: We present a new framework on generative modeling using the semi-dual formulation of Unbalanced Optimal Transport.

Abstract:

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}.

Submission Number: 6621