Convergence analysis of Schrödinger-Föllmer samplers without convexity

The Schrödinger-Föllmer sampler (SFS; see Huang et al. (2025)) is a novel and efficient approach for sampling from potentially unnormalized distributions without requiring ergodicity. The SFS is based on the Euler-Maruyama discretization of the Schrödinger-Föllmer diffusion process: (Formula presented.) on the unit interval, which transports the degenerate distribution at time zero to the target distribution at time one. In Huang et al. (2025), the consistency of the SFS is established under the restricted assumption that the potential U(x, t) is uniformly (in t) strongly convex in x. In this paper, we provide a non-asymptotic error bound for the SFS in Wasserstein distances under smoothness and boundedness conditions on the density ratio of the target distribution over the standard normal distribution, without requiring the strong convexity of the potential.