  We provide convergence guarantees in Wasserstein distance for a variety of
variance-reduction methods: SAGA Langevin diffusion, SVRG Langevin diffusion
and control-variate underdamped Langevin diffusion. We analyze these methods
under a uniform set of assumptions on the log-posterior distribution, assuming
it to be smooth, strongly convex and Hessian Lipschitz. This is achieved by a
new proof technique combining ideas from finite-sum optimization and the
analysis of sampling methods. Our sharp theoretical bounds allow us to identify
regimes of interest where each method performs better than the others. Our
theory is verified with experiments on real-world and synthetic datasets.
