  Sampling from probability distributions is an important problem in statistics
and machine learning, specially in Bayesian inference when integration with
respect to posterior distribution is intractable and sampling from the
posterior is the only viable option for inference. In this paper, we propose
Schr\"{o}dinger-F\"{o}llmer sampler (SFS), a novel approach for sampling from
possibly unnormalized distributions. The proposed SFS is based on the
Schr\"{o}dinger-F\"{o}llmer diffusion process on the unit interval with a time
dependent drift term, which transports the degenerate distribution at time zero
to the target distribution at time one. Comparing with the existing Markov
chain Monte Carlo samplers that require ergodicity, no such requirement is
needed for SFS. Computationally, SFS can be easily implemented using the
Euler-Maruyama discretization. In theoretical analysis, we establish
non-asymptotic error bounds for the sampling distribution of SFS in the
Wasserstein distance under suitable conditions. We conduct numerical
experiments to evaluate the performance of SFS and demonstrate that it is able
to generate samples with better quality than several existing methods.
