mlsanityData to 7 Oct 2026

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

arXiv 2602.11711 ↗First posted 12 Feb 2026stat.ML cs.LG cs.NAcited by 0

On the map: Diffusion models → Inverse problems and image restoration

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.

Key facts. No citing papers in the map yet (data through 7 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.

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6 of 29 references.

Closest ancestors · 4

Same direction, newest first

  1. 2026A Gibbs posterior sampler for inverse problem based on prior diffusion model11 Feb
  2. 2024Gaussian is All You Need: A Unified Framework for Solving Inverse Problems via Diffusion Posterior Sampling13 Sep
  3. 2023GibbsDDRM: A Partially Collapsed Gibbs Sampler for Solving Blind Inverse Problems with Denoising Diffusion Restoration30 Jan
  4. 2022Diffusion Posterior Sampling for General Noisy Inverse Problems29 Sep

Other references · 2

  1. 2024Tutorial on Diffusion Models for Imaging and Visioncited by 49
  2. 2018Model Selection Techniques -- An Overviewcited by 36

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  5. 2025Injecting Measurement Information Yields a Fast and Noise-Robust Diffusion-Based Inverse Problem Solver
  6. 2024Enhancing Diffusion Models for Inverse Problems with Covariance-Aware Posterior Sampling
  7. 2026Noise-Adaptive Diffusion Sampling for Inverse Problems Without Task-Specific Tuning
  8. 2024Taming Score-Based Diffusion Priors for Infinite-Dimensional Nonlinear Inverse Problems