Scalable diffusion posterior sampling in infinite-dimensional inverse problems

• URL: http://arxiv.org/abs/2405.15643v2
• Date: Mon, 03 Feb 2025 08:49:31 GMT
• Title: Scalable diffusion posterior sampling in infinite-dimensional inverse problems
• Authors: Fabian Schneider, Duc-Lam Duong, Matti Lassas, Maarten V. de Hoop, Tapio Helin,
• Abstract summary: We propose a scalable diffusion posterior sampling (SDPS) method to bypass forward mapping evaluations during sampling. The approach is shown to generalize to infinite-dimensional diffusion models and is validated through rigorous convergence analysis and high-dimensional CT imaging experiments.
• Score: 5.340736751238338
• License:
• Abstract: Score-based diffusion models (SDMs) have emerged as a powerful tool for sampling from the posterior distribution in Bayesian inverse problems. However, existing methods often require multiple evaluations of the forward mapping to generate a single sample, resulting in significant computational costs for large-scale inverse problems. To address this issue, we propose a scalable diffusion posterior sampling (SDPS) method to bypass forward mapping evaluations during sampling by shifting computational effort to an offline training phase, where a task-dependent score is learned based on the forward mapping. Crucially, the conditional posterior score is then derived from this trained score using affine transformations, ensuring no conditional score approximation is needed. The approach is shown to generalize to infinite-dimensional diffusion models and is validated through rigorous convergence analysis and high-dimensional CT imaging experiments.

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