  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 ar$ 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.
