(Oxy)hydroxides such as portlandite (Ca(OH)2), boehmite (γ-AlOOH), and gibbsite (γ-Al(OH)3) have been shown to produce and store dihydrogen or its precursor, the H atom when subjected to ionizing radiation. In this study, we investigate the diffusion of H2 and the associated lattice expansion within these three minerals using molecular simulations. The crystal structure of all three (oxy)hydroxides dilates linearly with the number of H2 molecules introduced, up to approximately 0.5 H2 per nm3. The energy barriers between hopping sites are compared with available data from quantum simulations for boehmite and gibbsite, and are provided for the first time for portlandite. H2 diffusion in these materials is shown to be subdiffusive, which might explain why such systems have to be activated, for example, by heating, to release the H2 molecules. Nevertheless, simulations also show that each system has its own specific behavior related to anisotropy in diffusion: H2 is effectively trapped in gibbsite, shows 1D diffusion in boehmite, and 2D diffusion in portlandite. H2 migration can be observed under experimentally attainable timescales in defect-free boehmite and portlandite, but not in gibbsite below 100°C. The affinity of H2 with the bulk mineral (quantified using a damping factor multiplied to the potential well energy of the H2 force field) together with the considerations about the connectivity of interstitial sites explains the subdiffusive behavior in the minerals studied.