  In order to sample from an unnormalized probability density function, we
propose to combine continuous normalizing flows (CNFs) with
rejection-resampling steps based on importance weights. We relate the iterative
training of CNFs with regularized velocity fields to a JKO scheme and prove
convergence of the involved velocity fields to the velocity field of the
Wasserstein gradient flow (WGF). The alternation of local flow steps and
non-local rejection-resampling steps allows to overcome local minima or slow
convergence of the WGF for multimodal distributions. Since the proposal of the
rejection step is generated by the model itself, they do not suffer from common
drawbacks of classical rejection schemes. The arising model can be trained
iteratively, reduces the reverse Kulback-Leibler (KL) loss function in each
step, allows to generate iid samples and moreover allows for evaluations of the
generated underlying density. Numerical examples show that our method yields
accurate results on various test distributions including high-dimensional
multimodal targets and outperforms the state of the art in almost all cases
significantly.
