  A diffusion process for charge distributions in a phase space is examined.
The corresponding charge moves in a force field and under an action of a random
field. There are the diffusion motions for coordinates and for momenta. In our
model, an inner state of the charge is defined by a complex vector. The vector
rotates with a great constant angular velocity with respect to the proper time
of the charge. A state of the diffusion process is a (complex-valued) wave
function on the phase space. As in quantum mechanics, we assume that, for the
wave functions, the superposition principle holds. The diffusion process
averages out vectors of inner states from different points of the phase space.
A differential equation for this diffusion process is founded and examined. We
demonstrate that the motion (described by this process) decomposes into a fast
motion and a slow motion. The fast motion reduces an arbitrary wave function to
a function from a subspace whose elements are parameterized by complex-valued
functions of coordinates. The slow motion occurs in this subspace and it is
described by the Schr\''odinger equation. The parameters of the suggested model
are estimated. The duration of the fast motion is of order $10^{-11}$ s.
