  We present an extended microcanonical Lanczos method (MCLM) for a direct
evaluation of the diffusion constant and its frequency dependence within the
disordered Anderson model of noninteracting particles. The method allows to
study systems beyond $10^6$ sites and we present results for diffusion in
hypercubic lattices in $ d = 3- 7$ dimensions. Below the transition to
localization, where we confirm dynamical scaling behaviour, of interest is a
wide region of incoherent diffusion, similar to percolating phenomena and to
interacting many-body localized systems.
