Proximal-Based Generative Modeling for Bayesian Inverse Problems

2026-05-13

AI Summary

This work addresses the performance bottleneck in score-based diffusion models for Bayesian inverse problems, where the intractability of the likelihood score hinders effective inference. To overcome this limitation, the authors propose the Proximal Generative Modeling (PGM) framework, which leverages the theoretical equivalence between Gaussian convolution and Moreau–Yosida regularization to devise a sampling mechanism that bypasses explicit likelihood evaluation. Central to this approach is the introduction of the Moreau score and a corresponding matching strategy, enabling the learning of proximal operators using only prior samples. The PGM framework eliminates early-stopping bias and ensures non-asymptotic convergence, achieving substantial improvements over state-of-the-art methods in both reconstruction quality and sampling efficiency.

Abstract

Score-based diffusion models demonstrate superior performance in generative tasks but encounter fundamental bottlenecks in inverse problems due to the analytical intractability of the time-dependent likelihood score. To bridge this gap, we propose a novel proximal-based generative modeling (PGM) framework that rigorously circumvents explicit likelihood evaluation. Our framework is built upon a theoretical equivalence between Gaussian convolution in diffusion processes and Moreau-Yosida regularization in nonsmooth optimization. This enables a new sampling mechanism driven by the proposed Moreau score, which admits a closed-form expression via proximal operators. Moreover, we introduce Moreau score matching to learn the proximal operators that rely solely on samples drawn from the prior distribution. Theoretically, PGM eliminates the early-stopping bias inherent in the score-based diffusion model and achieves non-asymptotic convergence. Experiments demonstrate that PGM significantly surpasses state-of-the-art methods in reconstruction quality and sampling time.

Problem

• Bayesian inverse problems
• score-based diffusion models
• likelihood score
• generative modeling
• inverse problems

Innovation

• proximal operator
• Moreau-Yosida regularization
• score-based diffusion
• Bayesian inverse problems
• Moreau score matching