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  1. Home
  3. Benchmarking Diffusion Annealing-based Bayesian Inverse Problem Solvers.
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  3. Benchmarking Diffusion Annealing-based Bayesian Inverse Problem Solvers.

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Benchmarking Diffusion Annealing-Based Bayesian Inverse Problem Solvers.

Evan Scope Crafts1, Umberto Villa1,2

  • 1Oden Institute for Computational Engineering and Sciences, The University of Texas at Austin, Austin, TX 78712 USA.

IEEE Open Journal of Signal Processing
|September 25, 2025

View abstract on PubMed

Summary
This summary is machine-generated.

This study introduces benchmark problems and a framework (BIPSDA) to evaluate diffusion model samplers for Bayesian inverse problems. This allows for rigorous assessment of uncertainty quantification in generative modeling applications.

Keywords:
Bayesian inferencediffusion modelsgenerative AImachine learningoptimizationposterior probabilityuncertainty quantification

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Area of Science:

  • Computational Mathematics
  • Machine Learning
  • Image Processing

Background:

  • Diffusion models are state-of-the-art generative models, increasingly used as priors in Bayesian inverse problems.
  • Optimal integration of diffusion models with likelihood functions for posterior sampling remains an open challenge.
  • Current evaluation methods struggle with rigorous uncertainty quantification due to unknown analytical priors.

Purpose of the Study:

  • To introduce benchmark problems with analytically known posteriors for evaluating diffusion model-based samplers.
  • To propose a general framework, Bayesian Inverse Problem Solvers through Diffusion Annealing (BIPSDA), for diffusion model-based posterior sampling.
  • To enable principled assessment of uncertainty quantification in diffusion model-based Bayesian inference.

Main Methods:

  • Developed three benchmark problems inspired by image inpainting, x-ray tomography, and phase retrieval.
  • Introduced the Bayesian Inverse Problem Solvers through Diffusion Annealing (BIPSDA) framework, unifying existing and novel algorithms.
  • Tested BIPSDA algorithms against benchmark problems to assess performance and uncertainty quantification.

Main Results:

  • The benchmark problems allow for approximate ground-truth posterior sampling for performance evaluation.
  • BIPSDA framework integrates various diffusion-based posterior sampling approaches.
  • Evaluations provided insights into the strengths and limitations of current diffusion model-based posterior samplers.

Conclusions:

  • The proposed benchmark problems offer a standardized platform for future development of diffusion model-based samplers.
  • The BIPSDA framework facilitates the development and evaluation of new algorithms for Bayesian inverse problems.
  • This work advances the rigorous evaluation of uncertainty quantification in generative modeling for inverse problems.