On the Equivalence of Consistency-Type Models: Consistency Models,
  Consistent Diffusion Models, and Fokker-Planck Regularization
Chieh-Hsin Lai Yuhta Takida Toshimitsu Uesaka Naoki Murata Yuki Mitsufuji Stefano Ermon
The emergence of various notions of ``consistency'' in diffusion models has
garnered considerable attention and helped achieve improved sample quality,
likelihood estimation, and accelerated sampling. Although similar concepts have
been proposed in the literature, the precise relationships among them remain
unclear. In this study, we establish theoretical connections between three
recent ``consistency'' notions designed to enhance diffusion models for
distinct objectives. Our insights offer the potential for a more comprehensive
and encompassing framework for consistency-type models.