Title: Partial Diffusion Suffices: Solving General Inverse Problems via Score Evolution
Primary area: generative models
Keywords: image recostruction; diffusion model;

Abstract: Despite rapid advancements, pre-trained diffusion models still face dual challenges in solving inverse problems. On the one hand, current methods depend heavily on iterative optimization of the complete reverse diffusion chain, leading to difficulties in balancing manifold preservation and measurement constraints, especially under complex scenarios. On the other hand, strong assumptions about noise characteristics are necessitated, limiting their applicability in most practices. With the signal-noise variation of the diffusion score theoretically analyzed, this study proposes a plug-in alternative, dubbed Partial Diffusion with Score Evolution (PDSE), which optimizes the solution space by reconstructing a partial iterative path of the reverse diffusion flow. First, with the signal-noise equilibrium point of the score function derived, the critical diffusion steps are precisely identified, which preserve essential generative capabilities while controlling the propagation range of evolving errors. Second, by employing a standardized optimization approach, the iterative programme could suppress interference from noise of varying types and intensities. Extensive experiments across diverse scenarios demonstrate that PDSE significantly enhances adherence to measurement constraints while ensuring manifold feasibility, particularly exhibiting robust performance in nonlinear inverse scenarios with unknown noise characteristics. The aonoymous code is available on \href{https://anonymous.4open.science/r/code-of-PDSE}{https://anonymous.4open.science/r/code-of-PDSE}.