A2PS: Solving Noisy Inverse Problems via Asymptotically Accurate Posterior Sampling in Diffusion and Flow Models

Training-free posterior sampling enables pretrained diffusion and flow models to solve inverse problems without task-specific retraining, but approximation errors can accumulate along the generative trajectory and bias the final distribution. We propose A2PS, a posterior sampling framework that progressively corrects these errors. Our key insight is that, near the end of generation, the distribution of the final clean sample conditioned on an intermediate state becomes increasingly well approximated by a Gaussian distribution, yielding an asymptotically accurate posterior score estimate. A2PS uses this estimate with Langevin dynamics to correct errors inherited from earlier steps. We establish the asymptotic accuracy of the posterior score and validate the resulting error-correction mechanism in a controlled setting. Across six noisy linear and nonlinear image inverse problems on ImageNet and FFHQ, with both pixel-space and latent-space models, A2PS achieves the best or near-best restoration quality among evaluated methods while also being the fastest across all tested tasks.