New algorithms for samplings and diffusion models

Drawing from the theory of stochastic differential equations, we introduce  a new sampling method for  known distributions, as well as a new algorithm for diffusion generative models with unknown distributions. Our approach is inspired by the concept of the reverse diffusion process, which has been widespread adoption in diffusion generative models. Furthermore, we compute the explicit convergence rate based on the smooth ODE flow. Numerical experiments exhibit the effectiveness of our method. In particular, unlike the traditional Langevin method, our sampling method does not require any regularity assumptions about the density function of the target distribution. We also apply it to the optimization problem.