We performed molecular dynamics simulations of the diffusion of interstitial He and H2O in ice Ih and found diffusion hops for these interstitial molecules from a stable site to an adjacent site. By observing the jumps of these diffusing species, we determined the jump frequencies, the crystal orientation dependence of the diffusion coefficients, and the diffusion activation energies. Most jumps are along the c axis, because the energy barrier for diffusion along the c axis is lower than that in the a-b plane. Furthermore, the diffusion mechanism for He significantly differ from that for H2O; interstitial H2O diffused by distorting the ice lattice, whereas He atom migrated by jumping from a stable interstitial site to an adjacent site without distorting the lattice. The transverse optic mode for translational lattice vibrations of the lattice surrounding the interstitial H2O shifts to high energy in comparison with that of the pure ice Ih. This upward shift is attributed to a strong coupling between localized translational vibrations of the interstitial H2O and lattice vibrations. The ice lattice is distorted by the translational vibration of the interstitial H2O, since the vibration energy of the mode is close to the energy region of the lattice vibrations of the ice Ih. We conclude that the localized vibrational motion of interstitial molecule is one of the dominant factors governing the diffusion mechanism of the molecule in the ice crystal.