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[Display omitted] • Group IVB and VB transition metal carbides have different mass diffusion mechanisms. • Vacancy clustering is much more favorable in group IVB than VB metal carbides. • Off-lattice diffusion mechanisms have lower activation energies than on-lattice. • Off-lattice diffusion might be the most dominant mechanism in the group IVB TMCs. Using ab initio simulations, we report potential metal atom diffusion mechanisms in the group IVB and VB transition metal carbides. By computing the metal vacancy formation energies of vacancy clusters, we find that a metal vacancy surrounded by six carbon vacancies is the lowest metal vacancy formation energy structure for the group IVB carbides while the lowest energy for the group VB carbides is a metal vacancy surrounded by two carbon vacancies. The vacancy cluster mechanisms reveal activation energies that are consistent with experiments in both TiC (group IVB) and TaC (group VB). We also report that an off-lattice diffusion mechanism, that is only energetically favorable in the group IVB transition metal carbides, has a lower formation energy than the regular vacancy cluster mechanism. This new mechanism shows lower formation energies for a given carbon vacancy concentration which indicates this off-lattice mechanism might be the most dominant metal-atom diffusion mechanism among the existing mechanisms proposed for the group IVB metal carbides. [ABSTRACT FROM AUTHOR]