Proximal-Based Generative Modeling for Bayesian Inverse Problems
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 More...
| Authors | Boyang Zhang, Zhiguo Wang, Ya-Feng Liu |
|---|---|
| Primary category | math.OC |
| Published | 13 May 2026 |
| Last updated at source | 27 May 2026 |
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