The present experiment aims to elucidate the energetics and geometry of translational diffusive motions exhibited by molecular hydrogen bound to carbon nanohorns. Previous experimental results (PRL 98, 215503 2007) show that, contrary to what is observed using nanotubes, molecular hydrogen remains bound to the these carbon nanostructures even after a thermal cycle from low to ambient temperature. Here we wish to deepen into the nature of these highly mobile bound states by means of analysis of the energetics of translational motions for temperatures that correspond to pure hydrogen to the solid, liquid and dense gas phases.