  We propose a sampling algorithm relying on a collective variable (CV) of
mid-size dimension modelled by a normalizing flow and using non-equilibrium
dynamics to propose full configurational moves from the proposition of a
refreshed value of the CV made by the flow. The algorithm takes the form of a
Markov chain with non-local updates, allowing jumps through energy barriers
across metastable states. The flow is trained throughout the algorithm to
reproduce the free energy landscape of the CV. The output of the algorithm are
a sample of thermalized configurations and the trained network that can be used
to efficiently produce more configurations. We show the functioning of the
algorithm first on a test case with a mixture of Gaussians. Then we
successfully test it on a higher dimensional system consisting in a polymer in
solution with a compact and an extended stable state separated by a high free
energy barrier.
