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

TL;DR

This paper introduces a new generative modeling approach using the semi-dual formulation of Unbalanced Optimal Transport, which improves robustness, training stability, and convergence over traditional OT-based methods.

Contribution

It presents a novel generative model leveraging UOT's semi-dual formulation, addressing OT's limitations with outliers and training difficulties, and provides theoretical analysis of divergence bounds.

Findings

Achieves state-of-the-art FID scores of 2.97 on CIFAR-10

Demonstrates improved robustness and training stability

Outperforms existing OT-based generative models

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}.