  Nonlinear diffusion equations of spectral transfer are systematically derived
for anisotropic magnetohydrodynamics in the regime of wave turbulence. The
background of the analysis is the asymptotic Alfv\'en wave turbulence equations
from which a differential limit is taken. The result is a universal
diffusion-type equation in ${\bf k}$-space which describes in a simple way and
without free parameter the energy transport perpendicular to the external
magnetic field ${\bf B_0}$ for transverse and parallel fluctuations. These
equations are compatible with both the thermodynamic equilibrium and the finite
flux spectra derived by Galtier et al. (2000); it improves therefore the model
built heuristically by Litwick \& Goldreich (2003) for which only the second
solution was recovered. This new system offers a powerful description of a wide
class of astrophysical plasmas with non-zero cross-helicity.
