Part II: Guaranteed and Efficient Sampling of Diffusion Models

We seek to develop a sharp, non-asymptotic convergence theory for mainstream diffusion-based samplers, leveraging these theoretical insights to design provably faster higher-order diffusion samplers, including SDE-based and ODE-based solvers. We will also investigate the capability of diffusion-based samplers to adapt to unknown low-dimensional data structures, exploiting adaptive parallel computing to provably speed up training and sampling.