i will present mcmc algorithms as optimization over the kl-divergence in the space of probabilities. by incorporating a momentum variable, i will discuss an algorithm which performs accelerated gradient descent over the kl-divergence. using optimization-like ideas, a suitable lyapunov function is constructed to prove that an accelerated convergence rate is obtained. i will then discuss how mcmc algorithms compare against variational inference methods in parameterizing the gradient flows in the space of probabilities and how it applies to sequential decision making problems.