We study the diffusion of classical hard-core particles in disordered lattices within the formalism of a quantum spin representation. This analogy enables an exact treatment of noninstantaneous correlation functions at finite particle densities in terms of single spin excitations in disordered ferromagnetic backgrounds. Applications to diluted chains and percolation clusters are discussed. It is found that density fluctuations in the former exhibit a stretched exponential decay while an anomalous power law asymptotic decay is conjectured for the latter.Instituto de Física La Plata