  We show that domain walls separating coexisting extremal current phases in
driven diffusive systems exhibit complex stochastic dynamics, with a
subdiffusive temporal growth of position fluctuations due to long-range
anticorrelated current fluctuations and a weak pinning at long times. This weak
pinning manifests itself in a saturated width of the domain wall position
fluctuations that increases sublinearly with the system size. As a function of
time $t$ and system size $L$, the width $w(t,L)$ exhibits a scaling behavior
$w(t,L)=L^{3/4}f(t/L^{9/4})$, with $f(u)$ constant for $u\gg1$ and $f(u)\sim
u^{1/3}$ for $u\ll1$. An Orstein-Uhlenbeck process with long-range
anticorrelated noise is shown to capture this scaling behavior. Results for the
drift coefficient of the domain wall motion point to memory effects in its
dynamics.
