  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.
