Measurement Embedded Schrödinger Bridge for Inverse Problems
This addresses the inference speed bottleneck for researchers and practitioners using diffusion models as priors in inverse problems like image restoration, though it appears incremental as an extension of Image-to-Image Schrödinger Bridge.
The paper tackles the slow inference speed of diffusion models in inverse problems by introducing Measurement Embedded Schrödinger Bridge (MESB), which establishes bridges between corrupted and clean image distributions given measurements, achieving superior performance in visual quality and quantitative metrics compared to existing Schrödinger Bridge-based solvers.
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.