  The incorporation of generative models as regularisers within variational
formulations for inverse problems has proven effective across numerous image
reconstruction tasks. However, the resulting optimisation problem is often
non-convex and challenging to solve. In this work, we show that score-based
generative models (SGMs) can be used in a graduated optimisation framework to
solve inverse problems. We show that the resulting graduated non-convexity flow
converge to stationary points of the original problem and provide a numerical
convergence analysis of a 2D toy example. We further provide experiments on
computed tomography image reconstruction, where we show that this framework is
able to recover high-quality images, independent of the initial value. The
experiments highlight the potential of using SGMs in graduated optimisation
frameworks.
