Recently, a new experimental setup for quick X-ray reflectivity (q-XRR) measurements was proposed, which is based on simultaneous recording of an X-ray reflectivity curve over all angles of interest. This new setup for q-XRR allows measurements to be done within seconds, thus permitting studies of the time evolution of chemical, thermal, and mechanical changes at the surfaces and interfaces of different materials. Since the q-XRR measurement setup utilizes an extended X-ray source and detector, it is important to develop models and to account for the following two effects: (i) diffuse scattering associated with different points of the source and (ii) sample curvature. Models accounting for both effects are presented, and their influences on interpretation of the q-XRR measurement results are discussed.