Sampling via Generalized Schrödinger–Föllmer Process

Generating samples from a complex probability distribution µ(x) on x ∈ R d is a fundamental problem in machine learning and statistics. In this work, we introduce a class of sampling schemes based on the generalized Schrödinger–Föllmer process (GSFP), a finite-horizon diffusion on t ∈ [0, 1] that transports a fixed initial point at t = 0 to a target distribution µ(x) at t = 1. The diffusion is governed by a stochastic differential equation whose drift admits a closed-form representation as an integral involving µ(x), which we approximate via annealed importance sampling. We evaluate the proposed approach on multimodal low-dimensional synthetic datasets and on a real-world physics problem involving the stochastic Allen–Cahn model. The results demonstrate that the GSFP-based algorithm generates samples that are competitive with those produced by state-of-the-art methods. Overall, our formulation provides a new pathway for constructing efficient diffusion-based samplers applicable to complex, high-dimensional, and multimodal distributions arising in large-scale real-world problems.