CuI is well-known to exhibit the superionic behaviour in the high temperature solid state (α-phase), where the mobile Cu ions migrate among the interstices in the f.c.c. sublattice formed by immobile I ions. Even in molten state, Cu ions has 8 times faster diffusion constant than I ions. Such asymmetric behavior between cations and anions can be caused by polarization of anions. From QENS, we distinguished three dynamical modes exist in molten phase, which are slowest diffusion of I ions, intermediate mode of Cu diffusion and fastest local dynamic mode like a rattling vibration. Deep inelastic neutron scattering by VESUVIO can allow us access directly kinetic energy of each constituent. By comparing non-superionic, superionic and liquid phases, the origin of existence of superionic phase regarded as partial melting or partial solidification can be revealed.