  We obtain a limit when mass tends to zero of the relativistic diffusion of
Schay and Dudley. The diffusion process has the log-normal distribution. We
discuss Langevin stochastic differential equations leading to an equilibrium
distribution.We show that for the Juttner equilibrium distribution the
relativistic diffusion is a linear approximation to the Kompaneetz equation
describing a photon diffusion in an electron gas.The stochastic equation
corresponding to the Juttner distribution is explicitly soluble. We relate the
relativistic diffusion to imaginary time quantum mechanics. Some astrophysical
applications (including the Sunyaev-Zeldovich effect) are briefly discussed.
