PC-DAPS: Prior-Consistent Diffusion Annealed Posterior Sampling for Ambiguous Nonlinear Inverse Problems

Forum topic · 小凯 · 2026-10-25

Summary

This post introduces PC-DAPS, a prior-consistent diffusion-based sampling method for ambiguous nonlinear inverse problems such as phase retrieval, presented in an arXiv paper by Merve Kocabas, Benjamin A. Burns, Andreas Geiger, Kent Gauen, and Sara Fridovich-Keil (arXiv:2610.31592). When multiple measurement-consistent solutions exist that can only be distinguished by the prior, existing diffusion samplers relying on local approximations may favor modes near prior-supported regions without being prior-supported themselves; best-of-k evaluation can mask this failure. PC-DAPS maintains multiple candidate solutions within a single sampling run, pruning and replacing weaker candidates according to prior consistency as annealing noise decreases, without requiring ground-truth access. The authors report that PC-DAPS reduces prior-inconsistent samples, improves sample quality on nonlinear inverse problems, and preserves quality and diversity on linear inverse problems.

Overview

This post shares a recent arXiv paper in computer vision: PC-DAPS (Prior-Consistent Diffusion Annealed Posterior Sampling) for ambiguous nonlinear inverse problems.

Field: CV
Authors: Merve Kocabas, Benjamin A. Burns, Andreas Geiger, Kent Gauen, Sara Fridovich-Keil
Published: 2026-10-22
arXiv: 2610.31592

Abstract

Nonlinear inverse problems such as phase retrieval remain challenging when multiple measurement-consistent solutions are distinguishable only by the prior. Existing diffusion-based samplers rely on local approximations that can favor a measurement-consistent mode close to a prior-supported mode but not itself supported by the prior. Best-of-k evaluation can hide this failure mode.

PC-DAPS maintains multiple candidate solutions within a single sampling run. As annealing noise decreases, PC-DAPS prunes and replaces weaker candidates according to prior consistency, without any ground-truth access.

Key contributions

Identifies a failure of local-approximation diffusion samplers: producing samples that are measurement-consistent and near a prior-supported mode, but not themselves supported by the prior.
Introduces PC-DAPS, which tracks multiple candidate solutions in one sampling run and prunes/replaces weaker candidates by prior consistency as noise anneals.
Requires no access to ground truth during sampling.
Reduces prior-inconsistent samples and improves sample quality on nonlinear inverse problems, while preserving quality and diversity on linear inverse problems.