Solving Diffusion Inverse Problems with Restart Posterior Sampling

Inverse problems—inferring an underlying signal or statefrom incomplete or noisy measurements—are fundamental to science andengineering. Recent approaches employ diffusion models as powerful im-plicit priors for such problems, owing to their ability to capture com-plex data distributions. However, existing diffusion-based methods forinverse problems often rely on strong approximations of the posteriordistribution, require computationally expensive gradient backpropaga-tion through the score network, or are restricted to linear measurementmodels.In this work, we propose Restart for Posterior Sampling (RePS), a gen-eral and efficient framework for solving both linear and non-linear in-verse problems using pre-trained diffusion models. RePS builds on theidea of restart-based sampling, previously shown to improve sample qual-ity in unconditional diffusion, and extends it to posterior inference. Ourmethod employs a conditioned ODE applicable to any differentiable mea-surement model and introduces a simplified restart strategy that con-tracts accumulated approximation errors during sampling. Unlike someof the prior approaches, RePS avoids backpropagation through the scorenetwork, substantially reducing computational cost. We demonstrate thatRePS achieves faster convergence and superior reconstruction qualitycompared to existing diffusion-based baselines across a range of inverseproblems, including both linear and non-linear settings.