An Euler discretization of the Langevin diffusion is known to converge to the global minimizers of certain convex and non-convex optimization problems. We show that this property holds for any suitably smooth diffusion and that different diffusions are suitable for optimizing different classes of convex and non-convex functions. This allows us to design diffusions suitable for globally optimizing convex and non-convex functions not covered by the existing Langevin theory. Our non-asymptotic analysis delivers computable optimization and integration error bounds based on easily accessed properties of the objective and chosen diffusion. Central to our approach are new explicit Stein factor bounds on the solutions of Poisson equations. We complement these results with improved optimization guarantees for targets other than the standard Gibbs measure.

Diffusion-based generative models, as first introduced by Sohl-Dickstein et al. (2015), have shown

Photorealistic generation is undergoing a period that future scholars may well compare to the enlightenment era.

In this paper, we point out that suboptimal noise-data mapping leads to slow training of diffusion models.

This work was completed while Xin Y uan was a PhD student at the University of Chicago.