  We study the breaking of integrability by a finite density of dilute
impurities, specifically the emerging diffusive transport. Provided the
distance between impurities (localized perturbations) is large, one would
expect that the scattering rates are additive, and therefore, the resistivity
is proportional to the number of impurities (the so-called Matthiessen's rule).
We show that this is, in general, not the case. If transport is anomalous in
the original integrable system without impurities, the diffusion constant in
the non-integrable system at low impurity density gets a nontrivial power-law
dependence on the impurity density, with the power being determined by the
dynamical scaling exponent of anomalous transport. We also find a regime at
high impurity density in which, counterintuitively, adding more impurities to
an already diffusive system increases transport rather than decreases it.
