You can now use diffusion models to solve inverse problems with mathematical guarantees—the algorithm switches between following the learned prior and using measurement data based on noise levels, making it both practical and provably correct.
This paper proposes PDDIM, a theoretically-grounded algorithm for solving inverse problems (like image restoration) using diffusion models. The method modifies standard DDIM sampling to incorporate measurement information through coordinate-wise updates based on signal-to-noise ratios, and proves it converges to the correct Bayesian posterior while being computationally efficient.