The anisotropic self-diffusion of molecular hydrogen in the multiple cage clathrasil losod (LOS) is modeled by means of molecular dynamics (MD) simulations of up to I us for the temperature range 900-1200 K while treating the framework as fully flexible. The LOS diffusion tensor is calculated employing an analytical method based on hopping rates. The diffusion in the c-direction of the unit cell is found to be approximately two times more rapid than in the a- and the b-directions, a characteristic of importance for the application of LOS as a membrane. The overall diffusion is based on five different hop types for which the individual hopping rates and diffusion barriers are calculated separately. We show explicitly that the shape and volume of the cages have a significant effect on the hopping rates and further that even small deformations of the circular Si6O6 apertures have a large influence on the energetic barrier for hydrogen diffusion. Compared to the single cage clathrasils dodecasil 3C (MTN) and sodalite (SOD), LOS has a lower diffusion rate. However, from a technical point of view this rate (at 573 K) is still fast enough for LOS to be interesting as a size-selective membrane or as a hydrogen-adsorption medium.