Title: Consistency-Guided Reverse Sampling for General Linear Inverse Problems
Primary area: probabilistic methods (Bayesian methods, variational inference, sampling, UQ, etc.)
Keywords: Diffusion Models, Inverse Problems, Machine Learning

Abstract: Diffusion models have recently demonstrated strong potential in solving inverse problems by leveraging the priors of learned data. However, the standard reverse sampling process often struggles to correct errors in the early stages, leading to suboptimal reconstructions, particularly in ill-posed or underdetermined settings. To overcome this issue, we present Consistency-Guided Reverse Sampling (CGRS), a novel framework that integrates measurement-consistency optimization into each reverse diffusion step. CGRS refines the intermediate denoised estimates by solving a linear least-squares problem, thereby improving consistency with the observed measurements. This correction mechanism mitigates error accumulation along the sampling trajectory and enhances overall reconstruction fidelity. Furthermore, CGRS naturally supports flexible acceleration by allowing the reverse process to start from a coarse optimization-based reconstruction, effectively reducing the number of reverse steps with negligible degradation in reconstruction quality. Experimental results in various linear inverse problems demonstrate that CGRS consistently yields superior performance.

TL;DR: CGRS integrates measurement-consistency optimization into diffusion sampling to improve consistency with measurements, enabling accurate and efficient inverse problem reconstruction.