Prediction and subtraction of multiple diffractions may include transforming previously acquired seismic data from a time-space domain to a transformed domain using a dictionary of compressive basis functions and separating, within the transformed previously acquired seismic data, a first portion and a second portion of the transformed previously acquired seismic data. Prediction and subtraction of multiple diffractions may also include predicting a plurality of multiple diffractions based on the separated first and second portions and adaptively subtracting the predicted multiple diffractions from the previously acquired seismic data. Prediction and subtraction of multiple diffractions may also include inverse transforming a particular seismic data set from the transformed domain to the time-space domain.