  The isotropic Heisenberg chain represents a particular case of an integrable
many-body system exhibiting superdiffusive spin transport at finite
temperatures. Here, we show that this model has distinct properties also at
finite magnetization $m\ne0$, even upon introducing the SU(2) invariant
perturbations. Specifically, we observe nonmonotonic dependence of the
diffusion constant ${\cal D}_0(\Delta)$ on the spin anisotropy $\Delta$, with a
pronounced maximum at $\Delta =1$. The latter dependence remains true also in
the zero magnetization sector, with superdiffusion at $\Delta=1$ that is
remarkably stable against isotropic perturbation (at least in finite-size
systems), consistent with recent experiments with cold atoms.
