# Measuring Effective Data Resolution in Guided Diffusion Posteriors

arXiv: https://arxiv.org/abs/2610.04422 · HTML: https://mlsanity.com/paper/2610.04422/

## Key facts

- No citing papers in the map yet (data through 14 Oct 2026).
- Placed in Inverse problems and image restoration, one of 14 directions in Diffusion models.
- Builds on 14 of its 28 references that are in the map.
- First posted on arXiv 3 Oct 2026.

## Placed in

- Diffusion models / [Inverse problems and image restoration](https://mlsanity.com/diffusion/inverse-problems-and-image-restoration/)

## Builds on (most cited first, 14 of 14)

- [Elucidating the Design Space of Diffusion-Based Generative Models](https://mlsanity.com/paper/2206.00364/) (2022)
- [Fourier Neural Operator for Parametric Partial Differential Equations](https://mlsanity.com/paper/2010.08895/) (2020)
- [Diffusion Posterior Sampling for General Noisy Inverse Problems](https://mlsanity.com/paper/2209.14687/) (2022)
- [Denoising Diffusion Restoration Models](https://mlsanity.com/paper/2201.11793/) (2022)
- [Zero-Shot Image Restoration Using Denoising Diffusion Null-Space Model](https://mlsanity.com/paper/2212.00490/) (2022)
- [Solving Inverse Problems in Medical Imaging with Score-Based Generative Models](https://mlsanity.com/paper/2111.08005/) (2021)
- [Accurate Uncertainties for Deep Learning Using Calibrated Regression](https://mlsanity.com/paper/1807.00263/) (2018)
- [Poseidon: Efficient Foundation Models for PDEs](https://mlsanity.com/paper/2405.19101/) (2024)
- [High-dimensional Bayesian inference via the Unadjusted Langevin Algorithm](https://mlsanity.com/paper/1605.01559/) (2016)
- [DiffusionPDE: Generative PDE-Solving Under Partial Observation](https://mlsanity.com/paper/2406.17763/) (2024)
- [Score-based Data Assimilation](https://mlsanity.com/paper/2306.10574/) (2023)
- [Optimal low-rank approximations of Bayesian linear inverse problems](https://mlsanity.com/paper/1407.3463/) (2014)
- [FunDiff: Diffusion Models over Function Spaces for Physics-Informed Generative Modeling](https://mlsanity.com/paper/2506.07902/) (2025)
- [Linearization Turns Neural Operators into Function-Valued Gaussian Processes](https://mlsanity.com/paper/2406.05072/) (2024)

## Abstract (arXiv)

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, dofref, and the resolution realised by the sampler, dofsamp. A perturbation estimator measures dofsamp 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.