We have developed a migration scheme that can image weak diffractions in time. This significantly contributes to conventional interpretation in detecting small-scale faults and heterogeneities. The proposed scheme images diffractions using the shot and opening-angle gathers generated by prestack time migration (PSTM). Here, the shot and opening-angle gather represents a 2D migrated gather in terms of shot locations and opening angles between the incident- and scattered-rays. We muted the Fresnel zones related to reflections, corrected phases of diffractions, and enhanced diffractions in the migrated gathers. As a result, the proposed diffraction PSTM can image diffractions with and without phase-reversal. Moreover, the weak diffractions tangent to reflections can be clearly imaged. Diffraction PSTM can update migration velocities according to behaviors of reflection and diffraction events in the migrated gathers by scanning, thus overcoming a crucial problem in diffraction imaging. The reflector dips used in diffraction PSTM are obtained by picking the angles related to reflections in the shot and opening-angle gathers for a partial migration. Synthetic and field data tests demonstrate the validity of diffraction PSTM.