Covariance-Corrected Diffusion Models for Solving Inverse Problems

Diffusion models have become powerful tools for image generation as well as for solving inverse problems. However, existing posterior sampling approaches that enforce data consistency during reverse sampling often suffer from inefficient or inaccurate likelihood approximations. This leads to suboptimal and sometimes inaccurate reconstructions. We address these limitations with a novel unified likelihood approximation method that incorporates a covariance correction term. Our approach improves posterior convergence without requiring diffusion model gradient propagation. This allows our method to greatly enhance computational efficiency. Experimental results demonstrate that our method achieves competitive performance across a diverse set of inverse problems and natural image datasets, consistently producing high-quality reconstructions while significantly reducing computational costs compared to existing approaches. ¹