We propose a surrogate function for efficient use of score-based priors for Bayesian inverse imaging. Recent work turned score-based diffusion models into probabilistic priors for solving ill-posed imaging problems by appealing to an ODE-based log-probability function. However, evaluating this function is computationally inefficient and inhibits posterior estimation of high-dimensional images. Our proposed surrogate prior is based on the evidence lower-bound of a score-based diffusion model. We demonstrate the surrogate prior on variational inference for efficient approximate posterior sampling of large images. Compared to the exact prior in previous work, our surrogate prior accelerates optimization of the variational image distribution by at least two orders of magnitude. We also find that our principled approach achieves higher-fidelity images than non-Bayesian baselines that involve hyperparameter-tuning at inference. Our work establishes a practical path forward for using score-based diffusion models as general-purpose priors for imaging.

翻译：我们提出一种替代函数，以实现基于分数先验在贝叶斯逆成像中的高效应用。现有研究通过利用基于常微分方程的对数概率函数，将分数扩散模型转化为解决病态成像问题的概率先验。然而，该函数的计算效率低下，阻碍了高维图像的后验估计。本文提出的替代先验基于分数扩散模型的证据下界，并将其用于变分推断中，以实现对大型图像的高效近似后验采样。与先前工作中的精确先验相比，我们的替代先验将变分图像分布的优化速度提升了至少两个数量级。此外，我们的原理性方法相较于需要推理时超参数调优的非贝叶斯基线方法，能够生成更高保真度的图像。本研究为将分数扩散模型作为通用先验应用于成像领域提供了实用路径。