  Drawing from the theory of stochastic differential equations, we introduce a
novel sampling method for known distributions and a new algorithm for diffusion
generative models with unknown distributions. Our approach is inspired by the
concept of the reverse diffusion process, widely adopted in diffusion
generative models. Additionally, we derive the explicit convergence rate based
on the smooth ODE flow. For diffusion generative models and sampling, we
establish a dimension-free particle approximation convergence result. Numerical
experiments demonstrate the effectiveness of our method. Notably, unlike the
traditional Langevin method, our sampling method does not require any
regularity assumptions about the density function of the target distribution.
Furthermore, we also apply our method to optimization problems.
