  We study the creep dynamics of a two-dimensional interface driven through a
periodic potential using dynamical renormalization group methods. We find that
the nature of weak-drive transport depends qualitatively on whether the
temperature $T$ is above or below the equilibrium roughening transition
temperature $T_c$. Above $T_c$, the velocity-force characteristics is Ohmic,
with linear mobility exhibiting a jump discontinuity across the transition. For
$T \le T_c$, the transport is highly nonlinear, exhibiting an interesting
crossover in temperature and weak external force $F$. For intermediate drive,
$F>F_*$, we find near $T_c^{-}$ a power-law velocity-force characteristics
$v(F)\sim F^\sigma$, with $\sigma-1\propto \tilde{t}$, and well-below $T_c$,
$v(F)\sim e^{-(F_*/F)^{2\tilde{t}}}$, with $\tilde{t}=(1-T/T_c)$. In the limit
of vanishing drive ($F\ll F_*$) the velocity-force characteristics crosses over
to $v(F)\sim e^{-(F_0/F)}$, and is controlled by soliton nucleation.
