We use a classical transition state theory (TST) to calculate the diffusion constant for noble gas atoms through silica sodalite. Due to the restrictive geometry of the transition state, diffusion of Ne and Ar is energy-activated at room temperature, but the diffusion of He is limited by entropy. The small mass of He suggests that a quantum TST must be employed. Path integral Monte Carlo is used to perform the relevant sampling, and quantum and classical diffusivities are compared. Comparison reveals a competition between tunneling and diffraction of the quantum mechanical He atom. A pairwise centroid pseudopotential is developed for the guest-host atom pair, and the effective potential energy and TST rate are compared with that of direct quantum TST.