# Estimation of instrument and noise parameters for inverse problem based on prior diffusion model

arXiv: https://arxiv.org/abs/2602.11711 · HTML: https://mlsanity.com/paper/2602.11711/

## 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 6 of its 29 references that are in the map.
- First posted on arXiv 12 Feb 2026.

## Placed in

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

## Builds on (most cited first, 6 of 6)

- [Diffusion Posterior Sampling for General Noisy Inverse Problems](https://mlsanity.com/paper/2209.14687/) (2022)
- [GibbsDDRM: A Partially Collapsed Gibbs Sampler for Solving Blind Inverse Problems with Denoising Diffusion Restoration](https://mlsanity.com/paper/2301.12686/) (2023)
- [Tutorial on Diffusion Models for Imaging and Vision](https://mlsanity.com/paper/2403.18103/) (2024)
- [Model Selection Techniques -- An Overview](https://mlsanity.com/paper/1810.09583/) (2018)
- [Gaussian is All You Need: A Unified Framework for Solving Inverse Problems via Diffusion Posterior Sampling](https://mlsanity.com/paper/2409.08906/) (2024)
- [A Gibbs posterior sampler for inverse problem based on prior diffusion model](https://mlsanity.com/paper/2602.11059/) (2026)

## Abstract (arXiv)

This article addresses the issue of estimating observation parameters (response and error parameters) in inverse problems. The focus is on cases where regularization is introduced in a Bayesian framework and the prior is modeled by a diffusion process. In this context, the issue of posterior sampling is known to be thorny, and a recent paper proposes a notably simple and effective solution. Additionally, it opens an remarkable flexibility when it comes to estimating observation parameters. The proposed strategy enables to define an optimal estimator for both observation parameters and image of interest. Furthermore, the strategy provides a means for uncertainty quantification. In addition, MCMC algorithms allow for the computation of estimates and properties of posteriors, while offering some guarantees. The paper presents several numerical experiments that clearly confirm the computational efficiency and the quality of both estimates and uncertainty quantification.