  Diffusive scaling of position moments and a central limit theorem are
obtained for the mean position of a quantum particle hopping on a cubic lattice
and subject to a random potential consisting of a large static part and a small
part that fluctuates stochastically in time. If the static random potential is
strong enough to induce complete localization in the absence of time dependent
noise, then the diffusion constant is shown to go to zero proportional to the
square of the strength of the time dependent part.
