Some materials with the fluorite structures show a pronounced specific heat anomaly well below their melting temperature. This anomaly is a consequence of lattice disorder and is associated with the onset of fast-ion conduction. This paper presents the results of a series of experiments in which the coherent diffuse quasielastic neutron scattering from single crystals of three such fluorite compounds PbF2, SrCl2 and CaF2, was investigated. The diffuse scattering intensity, and its energy width, increases with temperature into the fast-ion phase, and when integrated over energy transfer the intensity exhibits a characteristic variation with scattering vector, falling on an anisotropic shell in reciprocal space and peaking in certain directions. The diffuse intensity indicates that dynamic correlations exist between the defective anions in the fast-ion-phase. A model of short-lived clusters comprising anion Frenkel interstitials, anion vacancies and relaxed anions has been developed which satisfactorily accounts for the distribution of intensity.