A method for computing unimolecular reaction rate constants in the IVR-limited regime is presented. It is based on Kramers' energy diffusion theory, with the reaction coordinate taken as the subsystem and the rest of the vibrational modes as the bath. Applications to some bond fission reactions demonstrate that the method accurately predicts the rate constants for wide range of energies by using the result of a dynamical calculation of the reaction rate at a single energy to determine the friction coefficient. Examination of the energy exchange in the reaction coordinate provides a qualitative understanding of the validity of the approach for treating unimolecular reactions. Thus, the method provides a practical means of calculating reaction rates in the IVR-limited regime at considerable savings of computer time than that required by standard classical trajectory calculations.