In the non relativistic picture of diffusion, a particle moves a distance comparable to the mean free path $ l $ it is scattered to a random direction. If the velocity of the particle is $ v $, then the diffusion coefficient is

$ D \approx v l $

so increasing the velocity increases the diffusion coefficient. One could naively think that in the relativistic limit the largest possible diffusion coefficient is $ D < c l $, and increasing the energy of the particle further will not increase the diffusion coefficient because the velocity cannot exceed the speed of light $ c $. Moreover, the mean velocity would never be relativistic because even if the particle does move with velocity $ c $, after $ N $ collisions the average velocity would be $ c/\sqrt{N} $, which is barely relativistic after just two collisions.

These difficulties can be reconciled by relativistic beaming. This effect limits the scattering angle to $ \gamma^{-2} $, where $ \gamma $ is the Lorentz factor. Thus, it takes $ \gamma^{4} $ collision to scatter a particle by an angle of order unity. The relativistic diffusion coefficient is therefore

$ D \approx c l \gamma^4 $