We examine the effect on energy flow and unimolecular dissociation of anisotropic diffusion in quantum number space and dephasing, using a scaling approach to describe the energy flow and localization. This approach can be applied to systems with local couplings in the quantum number space of approximate normal modes. We find that anisotropy in the coefficient of diffusion on the constant energy surface can combine with anistropy in the finite extent of state space to produce results which mimic those of a lower dimensional isotropic system, due to the early saturation of rapidly relaxing modes. We discuss the diffusion which is caused by dephasing, for both delocalized and localized systems. The results for the energy flow dynamics are used to find corrections to the RRKM reaction rate caused by returns to the region of reactive states. We find that returns are enhanced near the transition to localized eigenstates, causing a greatly diminished average reaction rate. However, we also find that dephasing can cause the average reaction rate to increase over the value for an isolated system.