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arXiv · 2610.31592

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

Merve Kocabas·Benjamin A. Burns·Andreas Geiger·Kent Gauen·Sara Fridovich-Keil
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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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Merve Kocabas, Benjamin A. Burns, Andreas Geiger, Kent Gauen, Sara Fridovich-Keil. 2026-10-22. Beyond Best-of-$k$: Prior-Consistent DAPS for Ambiguous Nonlinear Inverse Problems. https://arxiv.org/abs/2610.31592

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