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We propose a surrogate function for efficient yet principled use ofscore-based priors in Bayesian imaging. We consider ill-posed inverse imagingproblems in which one aims for a clean image posterior given incomplete ornoisy measurements. Since the measurements do not uniquely determine a trueimage, a prior is needed to constrain the solution space. Recent work turnedscore-based diffusion models into principled priors for solving ill-posedimaging problems by appealing to an ODE-based log-probability function.However, evaluating the ODE is computationally inefficient and inhibitsposterior estimation of high-dimensional images. Our proposed surrogate prioris based on the evidence lower bound of a score-based diffusion model. Wedemonstrate the surrogate prior on variational inference for efficientapproximate posterior sampling of large images. Compared to the exact prior inprevious work, our surrogate accelerates optimization of the variational imagedistribution by at least two orders of magnitude. We also find that ourprincipled approach gives more accurate posterior estimation thannon-variational diffusion-based approaches that involve hyperparameter-tuningat inference. Our work establishes a practical path forward for usingscore-based diffusion models as general-purpose image priors.

Variational Bayesian Imaging with an Efficient Surrogate Score-based Prior