发表机构
Indian Institute of Technology Gandhinagar; University of Southern California（印度理工学院甘地讷格尔分校; 南加州大学）
机构由 AI 辅助整理，请以论文原文为准。AI 中文总结
本文提出有效数据分辨率度量，通过扰动估计器测量引导扩散采样器在逆问题中的实际数据决定程度，发现引导权重对信息传递影响显著且单一权重无法同时校正均值、散布和分辨率。
AI 中文摘要
引导扩散采样器越来越多地被用于从稀疏观测中重建物理场，但标准诊断并未说明重建中有多少部分实际上由数据决定。我们为黑盒生成后验引入了有效数据分辨率：即由逆问题保证的分辨率 $\mathrm{dof}_{\mathrm{ref}}$ 与采样器实现的分辨率 $\mathrm{dof}_{\mathrm{samp}}$ 之间的比较。一种扰动估计器仅通过采样器查询即可测量 $\mathrm{dof}_{\mathrm{samp}}$ 和空间映射 $R(x,x)$。我们针对精确参考验证了该估计器，并将其用于研究引导扩散。测量结果表明，引导权重可以强烈改变表观信息传递，即使具有精确的先验和分数，均值、散布和分辨率也不能通过单一权重联合校正，并且分辨率保真度并不能可靠地遵循引导规则的表观原则性。
英文摘要
Guided diffusion samplers are increasingly used to reconstruct physical fields from sparse observations, but standard diagnostics do not say how much of the reconstruction was actually determined by the data. We introduce effective data resolution for black-box generative posteriors: a comparison between the resolution warranted by the inverse problem, $\mathrm{dof}_{\mathrm{ref}}$, and the resolution realised by the sampler, $\mathrm{dof}_{\mathrm{samp}}$. A perturbation estimator measures $\mathrm{dof}_{\mathrm{samp}}$ and the spatial map $R(x,x)$ from sampler queries alone. We validate the estimator against exact references and use it to study guided diffusion. The resulting measurements show that guidance weight can strongly alter apparent information transfer, that mean, spread and resolution are not jointly corrected by one weight even with an exact prior and score, and that resolution fidelity does not follow reliably from the apparent principledness of a guidance rule.
CommentsNeurIPS 2026 Workshop on AI for Stochastic Dynamics
