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Cu2Se and Cu2S are excellent model systems of superionic conductors with large diffusion coefficients that have been reported to exhibit different solid-liquid-like Cu-ion diffusion. In this paper, we clarify the atomic dynamics of these compounds with temperature-dependent ab-initio molecular dynamics (AIMD) simulations and inelastic neutron scattering (INS) experiments. Using the dynamical structure factor and Van-Hove correlation function, we interrogate the jump-time, hopping length distribution and associated diffusion coefficients. In cubic-Cu2Se at 500 K, we find solid-like diffusion with Cu-jump lengths matching well the first-neighbour Cu-Cu distance of ~3 Å in the crystal, and clearly defined optic phonons involving Cu-vibrations. Above 700 K, the jump-length distribution becomes a broad maximum cantered around 4 Å, spanning the first and second neighbour lattice distances, and a concurrent broadening of the Cu-phonon density of states. Further, above 900 K, the Cu-diffusion becomes close to liquid-like, with distributions of Cu-atoms continuously connecting crystal sites, while the vibrational modes involving Cu motions are highly damped, though still not fully over-damped as in a liquid. At low temperatures, the solid-like diffusion is consistent with previous X-ray diffraction and quasielastic neutron scattering experiments, while the higher-temperature observation of the liquid-like diffusion is in agreement with previous AIMD simulations. We also report AIMD simulations in Cu2S in the hexagonal and cubic superionic phases, and observe similar solid and liquid-like diffusion at low- and high-temperatures, respectively. The calculated ionic-conductivity is in fair agreement with reported experimental values.