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Beyond Best-of-$k$: Prior-Consistent DAPS for Ambiguous Nonlinear Inverse Problems

Merve Kocabaş, Benjamin A. Burns, Andreas Geiger, Kent Gauen, Sara Fridovich-Keil · 2026 · arXiv (Cornell University)

DOI: 10.48550/arxiv.2610.31592 · cited by 0 works (OpenAlex) · open-access PDF

French

Les modèles de diffusion sont devenus des précurseurs forts pour résoudre les problèmes inverse. Cependant, les problèmes inverse non linéaires tels que la récupération de phase restent difficiles lorsque des solutions multiples de mesure cohérentes ne peuvent être distinguées que par le précédent; nous appelons ces mesures ambiguës. Les échantillons basés sur la diffusion existants s'appuient sur les approximations locales lors de la reconstruction. Pour une mesure ambiguë, ces approximations peuvent permettre aux orientations de mesure de favoriser un mode de mesure cohérent qui est proche d'un mode précédemment pris en charge, mais qui n'est pas lui-même pris en charge par le précédent. L'évaluation masque souvent ce type d'échec en signalant les meilleures approximations de $

Machine translation (Meta M2M100); the English original follows.

Abstract

Diffusion models have become strong priors for solving inverse problems. However, nonlinear inverse problems such as phase retrieval remain challenging when multiple measurement-consistent solutions are distinguishable only by the prior; we call such measurements ambiguous. Existing diffusion-based samplers rely on local approximations during reconstruction. For an ambiguous measurement, these approximations can allow measurement guidance to favor a measurement-consistent mode that is close to a prior-supported mode but is itself not supported by the prior. Evaluation often masks this type of failure by reporting the best-of-$k$ runs, where the best is selected by comparison to the ground truth. We introduce Prior-Consistent DAPS (PC-DAPS), a variant of Decoupled Annealing Posterior Sampling (DAPS) designed to address this failure case by maintaining multiple candidate solutions within a single sampling run. As annealing noise decreases, PC-DAPS prunes and replaces weaker candidates according to their prior consistency, without any ground-truth access. PC-DAPS reduces the incidence of prior-inconsistent samples and improves sample quality on nonlinear inverse problems while preserving sample quality and diversity on linear inverse problems.

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Topics: Inverse problem, Inverse, Nonlinear system, Mathematics, Applied mathematics, Mathematical optimization

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