  We study a class of optimization problems in the Wasserstein space (the space
of probability measures) where the objective function is \emph{nonconvex} along
generalized geodesics. When the regularization term is the negative entropy,
the optimization problem becomes a sampling problem where it minimizes the
Kullback-Leibler divergence between a probability measure (optimization
variable) and a target probability measure whose logarithmic probability
density is a nonconvex function. We derive multiple convergence insights for a
novel {\em semi Forward-Backward Euler scheme} under several nonconvex (and
possibly nonsmooth) regimes. Notably, the semi Forward-Backward Euler is just a
slight modification of the Forward-Backward Euler whose convergence is -- to
our knowledge -- still unknown in our very general non-geodesically-convex
setting.
