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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

German

Diffusionsmodelle sind zu starken Prioren für die Lösung von umgekehrten Problemen geworden. Allerdings bleiben nichtlineare umgekehrte Probleme wie Phase-Recovery herausfordernd, wenn mehrere Mess-konsistente Lösungen nur durch die vorherige unterscheidbar sind; wir nennen solche Messungen ambigu. Bestehende diffusionsbasierte Proben verlassen sich während der Rekonstruktion auf lokale Annäherungen. Für eine ambigue Messung können diese Annäherungen die Messanleitung erlauben, einen Mess-konsistenten Modus zu begünstigen, der nahe an einem vorherig unterstützten Modus liegt, aber selbst nicht von der vorherigen unterstützt wird. Bewertung maskiert oft diese Art von Versagen, indem sie die besten $-of-k$-Runs melden, wo die besten Proben im Vergleich zur Grundwahrheit ausge

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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