  At the spin transition point of $\nu=2/3$ quantum Hall states, nuclear spins
in a two-dimensional electron gas are polarized by an electric current. Using
GaAs/AlGaAs double-quantum-well samples, we first observed the spatial
diffusion of nuclear spin polarization between the two layers when the nuclear
spin polarization is current-induced in one layer. By numerical simulation, we
estimated the diffusion constant of the nuclear spin polarization to be $15 \pm
7$\,nm$^2$/s.
