PC-DAPS 改进扩散模型求解歧义非线性逆问题
Beyond Best-of-$k$: Prior-Consistent DAPS for Ambiguous Nonlinear Inverse Problems
一篇解决相位恢复这类歧义逆问题的新论文：单次采样里同时养多个候选解，按先验淘汰弱的，不用best-of-k跑多次。
Diffusion 模型已成为求解逆问题的常用先验，但在相位恢复等非线性逆问题中，多个符合测量的解只能靠先验区分，论文将这类测量称为 ambiguous。现有基于扩散的采样器依赖局部近似，可能收敛到靠近先验支持模式但本身不被先验支持的那个测量一致解。论文提出 Prior-Consistent DAPS（PC-DAPS），在单次采样中维护多个候选解，随退火噪声降低按先验一致性剪除和替换弱候选，全程不需要真实值。PC-DAPS 减少了先验不一致样本，在非线性逆问题上提升样本质量，同时在线性逆问题上保持质量与多样性。
Beyond Best-of-$k$: Prior-Consistent DAPS for Ambiguous Nonlinear Inverse Problems
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.