Before revision:  For (not-necessarily-strongly-) convex and L-smooth potentials, exponential convergence in \chi^2 divergence  is proved, with a rate analogous to  state-of-the-art results of underdamped Langevin dynamics, plus an additional acceleration. 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:  For (not-necessarily-strongly-) convex and L-smooth potentials, exponential convergence in \chi^2 divergence is proved, with a rate analogous to state-of-the-art results of underdamped Langevin dynamics, plus an additional acceleration\tilde{\mathcal{O}}}{\epsilon}) iteration complexity in 2-Wasserstein distance, same as underdamped Langevin dynamics, but with a reduced constant.