We study spin-diffusion effects within a continuously variable magnetization distribution, integrating with micromagnetics the diffusive model of Zhang and Li [Phys. Rev. Lett. 93, 127204 (2004)]. Current-driven wall motion is, in the steady velocity regime, shown to be adequately described by an effective nonlocal nonadiabatic parameter. This parameter is found to be 20% larger than its local counterpart for a vortex wall in a NiFe nanostrip and hardly modified for a transverse wall. This may account for the yet unexplained experimental evidence that vortex walls move more easily under current when compared with transverse walls. It is shown that this effective parameter can be derived from the domain wall structure at rest.