  We discuss the dissipative diffusion-type term of the form
$\mathbf{m}\times\nabla^2\partial_t\mathbf{m}$ in the phenomenological
Landau-Lifshitz equation of ferromagnetic precession, which describes enhanced
Gilbert damping of finite-momentum spin waves. This term arises physically from
itinerant-electron spin flows through a perturbed ferromagnetic configuration
and can be understood to originate in the ferromagnetic spin pumping in the
continuum limit. We develop a general phenomenology as well as provide
microscopic theory for the Stoner and s-d models of ferromagnetism, taking into
account disorder and electron-electron scattering. The latter is manifested in
our problem through the Coulomb drag between the spin bands. The spin diffusion
is identified in terms of the transverse spin conductivity, in analogy with the
Einstein relation in the kinetic theory.
