  We introduce ImitationFlow, a novel Deep generative model that allows
learning complex globally stable, stochastic, nonlinear dynamics. Our approach
extends the Normalizing Flows framework to learn stable Stochastic Differential
Equations. We prove the Lyapunov stability for a class of Stochastic
Differential Equations and we propose a learning algorithm to learn them from a
set of demonstrated trajectories. Our model extends the set of stable dynamical
systems that can be represented by state-of-the-art approaches, eliminates the
Gaussian assumption on the demonstrations, and outperforms the previous
algorithms in terms of representation accuracy. We show the effectiveness of
our method with both standard datasets and a real robot experiment.
