We present an energy diffusion theory approach for computing thermal and microcanonical unimolecular reaction rates by solving the general energy diffusion equation. The solution naturally provides the rates in the diffusion limit for fast reactions and the transition state theory (TST) limit for slow reactions. The reaction rates between the two limits can be easily obtained by solving a one-dimensional Schrodinger-like equation transformed from the diffusion equation. Employing a model system consisting of a set of harmonic oscillators interacting with a heat bath, the thermal rates from the low-temperature TST regime to the high-temperature diffusion regime are calculated to demonstrate their dependence on the size of the molecule. The approach also provides a practical means of obtaining microcanonical rates at considerable savings of computer time compared to trajectory simulations. The method is applied to the unimolecular dissociation of RDX (hexahydro-1,3,5-trinitro-1,3,5-triazine), and its accuracy is demonstrated by comparison with the results from trajectory and Monte Carlo variational transition state theory calculations.