Measuring Effective Data Resolution in Guided Diffusion Posteriors

2026-10-03

AI Summary

This study addresses the challenge of quantifying the actual degree to which data determines outcomes when using guided diffusion models for physical field reconstruction, proposing the concept of “effective data resolution.” Methodologically, it employs a sampler-query-based perturbation estimation technique that compares the reference degrees of freedom of the inverse problem with those of sampling realizations to evaluate the data information transfer capacity of black-box generative posteriors. This work defines and quantifies this metric for the first time, revealing the nonlinear influence of guidance weights on information transfer as well as the decoupling among the mean, variance, and resolution. Furthermore, it demonstrates that a single guidance weight cannot simultaneously correct all statistical quantities, and that principled guidance rules do not inherently guarantee resolution fidelity.

Abstract

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.

Problem

• guided diffusion
• effective data resolution
• sparse observations
• generative posteriors
• inverse problem

Innovation

• Effective Data Resolution
• Guided Diffusion Samplers
• Perturbation Estimator
• Black-box Generative Posteriors
• Inverse Problem