  Quantum transport of strongly correlated fermions is of central interest in
condensed matter physics. Here, we present first-principle nonequilibrium Green
functions results using $T$-matrix selfenergies for finite Hubbard clusters of
dimension $1,2,3$. We compute the expansion dynamics following a potential
quench and predict its dependence on the interaction strength and particle
number. We discover a universal scaling, allowing an extrapolation to
infinite-size systems, which shows excellent agreement with recent cold atom
diffusion experiments [Schneider et al., Nat. Phys. 8, 213 (2012)].
