  In this paper, we propose a unified framework of denoising score-based models
in the context of graduated non-convex energy minimization. We show that for
sufficiently large noise variance, the associated negative log density -- the
energy -- becomes convex. Consequently, denoising score-based models
essentially follow a graduated non-convexity heuristic. We apply this framework
to learning generalized Fields of Experts image priors that approximate the
joint density of noisy images and their associated variances. These priors can
be easily incorporated into existing optimization algorithms for solving
inverse problems and naturally implement a fast and robust graduated
non-convexity mechanism.
