The development of economical materials for use as adsorptive storage medium continues to be a major hurdle for meeting the US DOE requirements for acceptable storage and fuel cell systems. Two potential classes of materials for sorptive hydrogen storage are carbon(C) and metal oxide(MO) based where the adsorption can be broadly categorized as either: H2-physisorption, based on weak Van der Waals interactions; and chemisorption, caused by H2 dissociation. Numerous studies on C and MO based materials indicate that high adsorption capacity through H2 physisorption is rather unlikely at near-ambient temperatures, required for practical applications. Significant enhancement of H2 storage capacity can be acheive by doping/decorating the materials with small amounts of metals that act catalytically and create a spillover of the adsorbed molecules. Spillover refers to the transport of an active species adsorbed or formed on a first surface onto another surface that does not sorb or form the active species (under the same conditions). QENS will be used to characterize the onset and nature of translational diffusion of H2 on pure or Pd decorated ZnO and MgO.