Diffusivities in natural gas hydrates are important but elusive transport properties. We describe an efficient and versatile equilibrium path sampling (EPS) approach for computing free energies. We use EPS along with transmission coefficient calculations and kinetic monte carlo simulations, to estimate the methane diffusivity within a structure I hydrate crystal. The calculations support a water-vacancy assisted diffusion mechanism where the methane hops from an unoccupied "donor" cage to adjacent "acceptor" cage. Transmission coefficient calculations confirm features of the free energy surface and provide dynamically corrected rate constants. The rate constants from atomistic simulations are used to simulate self-diffusion with the Gillespie algorithm. Self-diffusion rates are lower than the Einstein estimate because of the lattice connectivity and methane's preference for large cages over small cages. From a computational perspective we demonstrate that EPS can compute free energies for a broader class of coordinates than umbrella sampling with molecular dynamics. From a technological perspective, we estimate an important diffusion constant that has been difficult to measure.