Adversarial Schr\"odinger Bridge Matching

TL;DR

This paper introduces a discrete-time iterative Markovian fitting method for Schr"odinger Bridge problems, significantly reducing inference steps by leveraging adversarial diffusion models, thus enabling efficient unpaired domain translation.

Contribution

It proposes a novel discrete-time IMF approach that replaces stochastic process learning with transition probability learning, compatible with Denoising Diffusion GANs, for faster inference.

Findings

Achieves comparable quality with fewer steps

Reduces inference time significantly

Compatible with existing adversarial models

Abstract

The Schr\"odinger Bridge (SB) problem offers a powerful framework for combining optimal transport and diffusion models. A promising recent approach to solve the SB problem is the Iterative Markovian Fitting (IMF) procedure, which alternates between Markovian and reciprocal projections of continuous-time stochastic processes. However, the model built by the IMF procedure has a long inference time due to using many steps of numerical solvers for stochastic differential equations. To address this limitation, we propose a novel Discrete-time IMF (D-IMF) procedure in which learning of stochastic processes is replaced by learning just a few transition probabilities in discrete time. Its great advantage is that in practice it can be naturally implemented using the Denoising Diffusion GAN (DD-GAN), an already well-established adversarial generative modeling technique. We show that our D-IMF procedure can provide the same quality of unpaired domain translation as the IMF, using only several generation steps instead of hundreds. We provide the code at https://github.com/Daniil-Selikhanovych/ASBM.