Flow Sampling: Efficient Sampling from Unnormalized Densities via Diffusion Models

Flow Sampling introduces a novel approach for sampling from unnormalized densities by leveraging diffusion models and flow matching. Unlike conventional diffusion models that depend on data samples, this technique operates in a data-free environment where the target distribution is characterized by a known energy function. The training goal relies on a noise sample and focuses on regressing to a denoising diffusion drift derived from the energy function. By employing the interpolant process, Flow Sampling reduces the frequency of energy function evaluations during training, enhancing efficiency and scalability. This framework also applies to Riemannian manifolds, facilitating diffusion-based sampling in curved spaces, thereby tackling the issue of expensive energy function evaluations prevalent in scientific computing and statistical physics.