Deterministic illumination diffractive-diffusers have nonperiodic short and medium-scale topography. Because of the deterministic locations of vertical sidewalls at the phase transition boundaries, over-coating diffractive diffusers with thin-film antireflection layers perturbs their function, resulting in performance deviations and nonuniformities. To mitigate these effects, we added antireflection random nanostructures on the surface of three different classes of fused-silica multiphase diffractive diffusers, using reactive-ion plasma etching. The diffusers were measured before and after the random nanostructures addition, using a polarized-laser scatterometer with a dynamic range of nine orders of magnitude. The bidirectional scatter distribution function was measured over the entire equatorial plane of incidence, to analyze the directionality of scattered light and the impact of the antireflective nanostructure presence on the optical performance of the diffusers. The overall reflectivity suppression was measured across the illumination patterns directions, as well as, across the entire 180-deg angle-sweep. The designed deterministic illumination patterns and their contrast were unaffected by the presence of the random antireflective structures, whereas Fresnel reflectivity was reduced by an order of magnitude on average.