DAPS++: Rethinking Diffusion Inverse Problems with Decoupled Posterior Annealing

Abstract

From a Bayesian perspective, score-based di_x001B_usion solves in-verse problems through joint inference, embedding the likelihood withthe prior to guide the sampling process. However, this formulation failsto explain its practical behavior: the prior o_x001B_ers limited guidance, whilereconstruction is largely driven by the measurement-consistency term,leading to an inference process that is e_x001B_ectively decoupled from thedi_x001B_usion dynamics. We show that the di_x001B_usion prior in these solversfunctions primarily as a warm initializer that places estimates near thedata manifold, while reconstruction is driven almost entirely by measure-ment consistency. Based on this observation, we introduce DAPS++,which fully decouples di_x001B_usion-based initialization from likelihood-drivenre_x001C_nement, allowing the likelihood term to guide inference more directlywhile maintaining numerical stability and providing insight into whyuni_x001C_ed di_x001B_usion trajectories remain e_x001B_ective in practice. By requiringfewer function evaluations (NFEs) and measurement-optimization steps,DAPS++ achieves high computational e_x001E_ciency and robust reconstruc-tion performance across diverse image restoration tasks.