Kramers's original paper on the diffusion model of chemical reactions was based on the consideration that only the barrier region determines the outcome of transmission over a barrier. Subsequently it became understood that Kramers's approach was identical to variational transition state theory (VTST) and as such used only thermodynamic information. Here, using Kramers's philosophy in conjunction with perturbation theory and the realization that the dynamics which is rate-determining usually occurs in the vicinity of the transition state leads to a novel stochastic rate theory in which the momentum change induced by the medium is the stochastic variable. A first successful application of the theory is to the old and challenging problem of motion over a cusped barrier. This has implications for the study of transition path time distributions as well as the theory of tunneling via nonadiabatic coupling.