arXiv:2602.11059v2 Announce Type: replace-cross Abstract: This paper addresses the issue of inversion in cases where (1) the observation system is modeled by a linear transformation and additive error, (2) the problem is ill-posed and regularization relies on a Bayesian strategy, (3)~the prior is modeled by a diffusion process adjusted on an available large set of examples. In this context, it is known that the issue of posterior sampling is a thorny one and the paper introduces a Gibbs algorithm. It appears that this avenue has not been explored, and we show that it is particularly effective
The paper introduces a novel Gibbs algorithm for posterior sampling in inverse problems with diffusion-model priors, addressing a current 'thorny issue' in Bayesian statistical modeling.
This contributes to the theoretical and practical foundations of AI, potentially enabling more robust and efficient solutions for complex inverse problems relevant across scientific and engineering domains.
A new method for tackling ill-posed inverse problems using diffusion models and MCMC sampling is introduced, potentially improving the accuracy and feasibility of previous approaches.
- · AI researchers
- · Machine learning engineers
- · Scientific computing sector
Improved performance in applications requiring inverse problem solutions, such as medical imaging, computer vision, and scientific discovery.
Accelerated development of AI systems that rely on accurately inferring underlying causes from observed data.
Enhanced AI capabilities across various industries, leading to new scientific breakthroughs and technological advancements.
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Read at arXiv cs.LG