Using extensive Brownian dynamics computer simulations, the long-time self-diffusion coefficient is calculated for Gaussian-core particles as a function of the number density. Both spherical and rod-like particles interacting via Gaussian segments are considered. For increasing concentration we find that the translational self-diffusion behaves non-monotonically reflecting the structural reentrance effect in the equilibrium phase diagram. Both in the limits of zero and infinite concentration, it approaches its short-time value. The microscopic Medina-Noyola theory qualitatively accounts for the translational long-time diffusion. The long-time orientational diffusion coefficient for Gaussian rods, on the other hand, remains very close to its short-time counterpart for any density. Some implications of the weak translation–rotation coupling for ultrasoft rods are discussed.