Measurement Embedded Schrödinger Bridge for Inverse Problems

Abstract

Score-based diffusion models are frequently employed as structural priors in inverse problems. However, their iterative denoising process, initiated from Gaussian noise, often results in slow inference speeds. The Image-to-Image Schrödinger Bridge (I${}^2$SB), which begins with the corrupted image, presents a promising alternative as a prior for addressing inverse problems. In this work, we introduce the Measurement Embedded Schrödinger Bridge (MESB). MESB establishes Schrödinger Bridges between the distribution of corrupted images and the distribution of clean images given observed measurements. Based on optimal transport theory, we derive the forward and backward processes of MESB. Through validation on diverse inverse problems, our proposed approach exhibits superior performance compared to existing Schrödinger Bridge-based inverse problems solvers in both visual quality and quantitative metrics.

14 pages, 2 figures, Neurips preprint