Diffusion of deuterium in indium is studied herein. In the temperature range 200–350 K, mass transfer is controlled predominantly by the mechanism of overbarrier atomic jumps; at temperatures from 80 to 120 K, by tunneling; whereas in the range from 120 to 200 K, there takes place a gradual transition from one migration mechanism to the other. These results are of fundamental significance since it is shown for the first time that quantum diffusion can be observed in a metal with a crystal lattice other than the body centered cubic one. Conditions are specified that are necessary for the observation of quantum diffusion of hydrogen: low values of Debye temperature, density of atomic packing in the lattice, and distance between the nearest equilibrium positions of hydrogen atoms. Moreover, data on the influence of point defects on hydrogen tunneling in solids are gained for the first time as well. The quantum diffusion coefficient is twice as high in the sample with enhanced vacancy concentration.