Among the many different types of molecules that form clathrate hydrates, H2 is unique as it can easily diffuse into and out of clathrate cages, a process that involves the physical-chemical interactions between guest (H2) and host (water) molecules, and is unlike any other molecular system. The dynamic and nano-scale process of H2 diffusion into binary structure II hydrates, where the large cages are occupied by larger molecules, was studied using molecular dynamics simulation. As the H2 molecules diffused from one cage to another, two types of diffusion processes were observed: (i) when moving between a pair of large cages, the H2 molecules pass through the central part of the hexagonal rings; (ii) however, when the H2 molecules move from a large cage to a small one, it requires one of the pentagonal rings to partially break, as this allows the H2 molecule to pass through the widened space. While the diffusion of H2 molecules between large cages was found to occur more frequently, the presence of SF6 molecules in the large cages was found to inhibit diffusion. Therefore, in order to attain higher H2 storage capacities in binary hydrates, it is suggested that there is an optimal number of large cages that should be occupied by SF6 molecules.