I will discuss a class of diffusion-based algorithms to draw samples from high-dimensional probability distributions given their unnormalized densities. Ideally, the method can transport samples from a Gaussian distribution to a specified target distribution in
finite time. The stochastic interpolants framework used to
derive a diffusion process, and also involves solving certain Hamilton-Jacobi-Bellman PDEs. These are solved using the theory of forward-backward stochastic differential equations (FBSDE) together with machine learning-based methods. Numerical experiments illustrating that the algorithm will also be discussed.
This is joint work with Anand Jerry George.