On the Equivalence of Consistency-Type Models: Consistency Models, Consistent Diffusion Models, and Fokker-Planck Regularization

It refers to a (diffusion) model that is explicitly designed to align with The emergence of various notions of "consistency" the underlying trajectory defined by an ordinary differential in diffusion models has garnered considerable equation (ODE), stochastic differential equation (SDE), or attention and helped achieve improved sample partial differential equation (PDE). In this study, we aim quality, likelihood estimation, and accelerated to provide a theoretical investigation into the relationships sampling. Although similar concepts have between these three consistency-type models. Under certain been proposed in the literature, the precise relationships mild assumptions, we will rigorously establish the equivalence among them remain unclear. In this of these independently developed concepts.