In the non relativistic picture of diffusion, a particle moves a distance comparable to the mean free path it is scattered to a random direction. If the velocity of the particle is , then the diffusion coefficient is
so increasing the velocity increases the diffusion coefficient. One could naively think that in the relativistic limit the largest possible diffusion coefficient is , and increasing the energy of the particle further will not increase the diffusion coefficient because the velocity cannot exceed the speed of light . Moreover, the mean velocity would never be relativistic because even if the particle does move with velocity , after collisions the average velocity would be , which is barely relativistic after just two collisions.
These difficulties can be reconciled by relativistic beaming. This effect limits the scattering angle to , where is the Lorentz factor. Thus, it takes collision to scatter a particle by an angle of order unity. The relativistic diffusion coefficient is therefore