In the present work we investigated how the sorbate loading controls the diffusion of spherically symmetric Lennard-Jones molecules in a cation-free zeolite of type LTA. This effect is studied by taking into account the mechanical flexibility of the framework, which allows for the energy relaxation of the sorbed molecules along with fluctuations of the window diameters. The number density of the adsorbed molecules was increased from 1 up to 15 methane molecules per cavity, which means from 8 up to 120 particles adsorbed in one unit cell. We have shown that the sorbate loading strongly alters the diffusion mechanism by inducing a transition at seven molecules per cavity from an increasing to a decreasing mobility regime.