  We explicitly calculate the density-density response function with conserving
vertex corrections for anisotropic multiband systems in the presence of
impurities including long-range disorder. The direction-dependence of the
vertex corrections is correctly considered to obtain the diffusion constant
which is given by the combination of the componentwise transport relaxation
times and velocities on the Fermi surface. We also investigate the diffusive
density response of various anisotropic systems, propose some empirical rules
for the corresponding diffusion constant, and demonstrate that it is crucial to
consider the component-dependence of the transport relaxation times to
correctly interpret the transport properties of anisotropic systems, especially
various topological materials with a different power-law dispersion in each
direction.
