  Bias plays an important role in the enhancement of diffusion in periodic
potentials. Using the continuous-time random walk in the presence of a bias, we
provide a novel mechanism for the enhancement of diffusion in a random energy
landscape. When the variance of the waiting time diverges, in contrast to the
bias-free case the dynamics with bias becomes superdiffusive. In the
superdiffusive regime, we find a distinct initial ensemble dependence of the
diffusivity. We show that the time-averaged variance converges to the
corresponding ensemble-averaged variance, i.e., ergodicity is preserved.
However, trajectory-to-trajectory fluctuations of the time-averaged variance
decay slowly. Our finding suggests that in the superdiffusive regime the
diffusivity for a non-equilibrium initial ensemble gradually increases to that
for an equilibrium ensemble when the start of the measurement is delayed,
corresponding to a rejuvenation of diffusivity.
