  We consider a simple quantum system subjected to a classical random force.
Under certain conditions it is shown that the noise-averaged Wigner function of
the system follows an integro-differential stochastic Liouville equation. In
the simple case of polynomial noise-couplings this equation reduces to a
generalized Fokker-Planck form. With nonlinear noise injection new ``quantum
diffusion'' terms arise that have no counterpart in the classical case. Two
special examples that are not of a Fokker-Planck form are discussed: the first
with a localized noise source and the other with a spatially modulated noise
source.
