The diffuse lattice model for liquid structure, due to Prins, produces certain lattice expansion representations of the scattering function S(k). These are compared with modified expansions derived from consideration of more general spatial random processes, in particular structural diffusion. The latter expansions are free from limitations of accuracy and inconsistency inherent in the former. Numerical results from the structural diffusion model are compared with recent calculations based on the Prins model. (C) 2002 Elsevier Science B.V. All rights reserved.