  We develop a linear response formalism for nuclear spin diffusion in a
dipolar coupled solid. The theory applies to the high-temperature,
long-wavelength regime studied in the recent experiments of Boutis et al.
[Phys. Rev. Lett. 92, 137201 (2004)], which provided direct measurement of
interspin energy diffusion in such a system. A systematic expansion of Kubo's
formula in the flip-flop term of the Hamiltonian is used to calculate the
diffusion coefficients. We show that this approach is equivalent to the method
of Lowe and Gade [Phys. Rev. 156, 817 (1967)] and Kaplan [Phys. Rev. B 2, 4578
(1970)], but has several calculational and conceptual advantages. Although the
lowest orders in this expansion agree with the experimental results for
magnetization diffusion, this is not the case for energy diffusion. Possible
reasons for this disparity are suggested.
