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. At discrete algorithm level, a dedicated discretization algorithm is proposed to simulate the Hessian-Free High-Resolution SDE in a cost-efficient manner. For log-strong-concave target measures, the proposed algorithm achieves\tilde{\mathcal{O}}}{\epsilon}) iteration complexity in 2-Wasserstein distance, same as underdamped Langevin dynamics, but with a reduced constant.