  We obtain a generalization of the relativistic diffusion of Schay and Dudley
for particles with spin. The diffusion equation is a classical version of an
equation for the Wigner function of an elementary particle. The elementary
particle is described by a unitary irreducible representation of the Poincare
group realized in the Hilbert space of wave functions in the momentum space.
The arbitrariness of the Wigner rotation appears as a gauge freedom of the
diffusion equation. The spin is described as a connection of a fiber bundle
over the momentum hyperbolic space (the mass-shell). Motion in an
electromagnetic field, transport equations and equilibrium states are
discussed.
