We study the effects of quantum corrections on transverse momentum broadening a fast parton passing through dense QCD matter. show that, at leading logarithmic accuracy distribution tends late times or equivalently for large system sizes $L$ to universal that only depends single scaling variable ${k}_{T}^{2}/{Q}_{s}^{2}$ where typical scale increases with time as $\mathrm{ln}\text{ }{Q}_{s}^{2}...