We examine the diffusion of methane in the metal organic frameworks M-2(dobdc) (M = Mg, Ni, Zn; dobdc(4-) = 2,5-diwddo-1,4-benzenedicarboxylate) as a function of methane loading through a combination of nuclear magnetic resonance and molecular dynamics simulations. At low gas densities, our results suggest that favorable CH4-CH4 interactions lower the free energy barrier for methane hopping between coordinatively unsaturated metal sites and thus enhance the translational motion of methane down the c-axis. At higher gas densities, CH4-CH4 interactions become more significant, CH4-CH4 collisions become more frequent, and the gas self-diffusion begins to decrease. Finally, we observe that the self-diffusion coefficient of methane is inversely related to the binding energy at the coordinatively unsaturated metal sites, such that diffusion is most rapid in the Zn-2(dobdc) framework.