We address the question of the microscopic origin of dissipation in collective motion of a quantum many--body system in the framework of a parametric random matrix approach to the intrinsic dynamics. We show that the fluctuation--dissipation theorem is generally violated and, moreover, energy diffusion has a markedly non--Gaussian character and the corresponding distribution has very long tails. Such features do not support a Langevin or Fokker--Planck approach to dissipation in collective nuclear motion