In this work, we propose a method to learn multivariate probability
distributions using sample path data from stochastic differential equations.
Specifically, we consider temporally evolving probability distributions (e.g.,
those produced by integrating local or nonlocal Fokker-Planck equations). We
analyze this evolution through machine learning assisted construction of a
time-dependent mapping that takes a reference distribution (say, a Gaussian) to
each and every instance of our evolving distribution. If the reference
distribution is the initial condition of a Fokker-Planck equation, what we
learn is the time-T map of the corresponding solution. Specifically, the
learned map is a multivariate normalizing flow that deforms the support of the
reference density to the support of each and every density snapshot in time. We
demonstrate that this approach can approximate probability density function
evolutions in time from observed sampled data for systems driven by both
Brownian and L\'evy noise. We present examples with two- and three-dimensional,
uni- and multimodal distributions to validate the method