The structure of a fluid is analyzed by considering a diffusion equation with the Giacomin-Lebowitz term for intermolecular interactions. This equation represents the differential mass balance with density functionals and the Metropolis algorithm for fluxes. Taking the equilibrium limit of this equation allows a new analytical solution for the direct correlation function over the entire range of fluid densities and temperatures. While this model predicts known behavior for both gas and liquid phases, approaching a phase transition (e.g., condensation of gas into liquid) results in a bifurcation and multiplicity of the direct correlation function. New solution predicts a sequence in the transformation of correlation functions from that of a gas to that of a liquid.