Before revision:  At the same time, the method also works for nonconvex potentials, for which we also establish exponential convergence as long as the potential satisfies a Poincar\'e inequality\tilde{\mathcal{O}}}{\epsilon}) iteration complexity in 2-Wasserstein distance, same as underdamped Langevin dynamics, but with a reduced constant.
After revision:  At the same time, the method also works for nonconvex potentials, for which we also establish exponential convergence as long as the potential satisfies a Poincar\'e inequality\tilde{\mathcal{O}}(\frac{\sqrt{d}{\epsilon}) iteration complexity in 2-Wasserstein distance, same as underdamped Langevin dynamics, but with a reduced constant.