  We show that Kompaneetz equation describing photon diffusion in an
environment of an electron gas, when linearized around its equilibrium
distribution, coincides with the relativistic diffusion discussed in recent
publications. The model of the relativistic diffusion is related to soluble
models of imaginary time quantum mechanics. We suggest some non-linear
generalizations of the relativistic diffusion equation and their astrophysical
applications (in particular to the Sunyaev-Zeldovich effect).
