  We present an analysis of diffusion in terms of the spontaneous density
fluctuations in a non-thermal two-species fluid modeled by a lattice gas
automaton. The power spectrum of the density correlation function is computed
with statistical mechanical methods, analytically in the hydrodynamic limit,
and numerically from a Boltzmann expression for shorter time and space scales.
In particular we define an observable -- the weighted difference of the species
densities -- whose fluctuation correlations yield the diffusive mode
independently of the other modes so that the corresponding power spectrum
provides a measure of diffusion dynamics solely. Automaton simulations are
performed to obtain measurements of the spectral density over the complete
range of wavelengths (from the microscopic scale to the macroscopic scale of
the automaton universe). Comparison of the theoretical results with the
numerical experiments data yields the following results: (i) the spectral
functions of the lattice gas fluctuations are in accordance with those of a
classical `non-thermal' fluid; (ii) the Landau-Placzek theory, obtained as the
hydrodynamic limit of the Boltzmann theory, describes the spectra correctly in
the long wavelength limit; (iii) at shorter wavelengths and at moderate
densities the complete Boltzmann theory provides good agreement with the
simulation data. These results offer convincing validation of lattice gas
automata as a microscopic approach to diffusion phenomena in fluid systems.
