  Diffusion is one of the physical processes allowed for describing the large
scale dark matter dynamics. At the same time, it can be seen as a possible
mechanism behind the interacting cosmologies. We study the non-linear spherical
"top-hat" collapse of dark matter which undergoes velocity diffusion into a
solvent dark energy field. We show constraints on the maximum magnitude allowed
for the dark matter diffusion. Our results reinforce previous analysis
concerning the linear perturbation theory.
