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

TL;DR

DAPS++ introduces a decoupled approach to diffusion inverse problems, improving efficiency and robustness by separating initialization from likelihood-driven refinement, and providing new insights into diffusion dynamics.

Contribution

It proposes a novel decoupled diffusion framework, DAPS++, that enhances efficiency and understanding of diffusion-based inverse problem solving.

Findings

DAPS++ requires fewer function evaluations and measurement steps.

It achieves robust image restoration across diverse tasks.

Provides insight into the role of diffusion prior as a warm initializer.

Abstract

From a Bayesian perspective, score-based diffusion solves inverse problems through joint inference, embedding the likelihood with the prior to guide the sampling process. However, this formulation fails to explain its practical behavior: the prior offers limited guidance, while reconstruction is largely driven by the measurement-consistency term, leading to an inference process that is effectively decoupled from the diffusion dynamics. We show that the diffusion prior in these solvers functions primarily as a warm initializer that places estimates near the data manifold, while reconstruction is driven almost entirely by measurement consistency. Based on this observation, we introduce \textbf{DAPS++}, which fully decouples diffusion-based initialization from likelihood-driven refinement, allowing the likelihood term to guide inference more directly while maintaining numerical stability and providing insight into why unified diffusion trajectories remain effective in practice. By requiring fewer function evaluations (NFEs) and measurement-optimization steps, \textbf{DAPS++} achieves high computational efficiency and robust reconstruction performance across diverse image restoration tasks.