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The kinetics of hydrogen diffusion in C15 cubic and C14 hexagonal TiCr2Hx (0 x 4) Laves-phase hydrogen storage alloys is investigated with density functional theory (DFT) and machine learning interatomic potentials (MLIPs). Generalized solid-state nudged elastic band calculations are conducted based on DFT for all symmetrically inequivalent paths between the first-nearest-neighbor face-sharing interstitial sites. The hydrogen migration barriers are substantially higher for the paths that require breaking a Ti–H bond than for those that require breaking a Cr–H bond. Molecular dynamics (MD) simulations with the MLIPs also demonstrate that hydrogen migration occurs more frequently within the hexagonal rings made of the A2B2 interstitial paths, each requiring the breaking of Cr–H bonds, than along the inter-ring paths. The diffusion coefficients of hydrogen obtained from the MD simulations reveal a non-monotonic dependence on hydrogen concentration, which is more pronounced at lower temperatures. Time-averaged radial distribution functions of hydrogen further show that hydrogen avoids face-sharing positions during diffusion and that the hydrogen occupancy at the second-nearest-neighbor edge-sharing positions increases with increasing hydrogen concentration. The diffusion coefficients of hydrogen within 400–1000 K follow an Arrhenius relationship, with activation barriers consistent with most experimental values. One-order of magnitude overestimation of diffusion coefficients compared with some experiments suggests a substantial impact of hydrogen trapping by defects such as Cr vacancies and Ti anti-sites in non-stoichiometric TiCr2 in experiments.