Seismic attributes play a crucial role in fault interpretation and mapping fracture density. Conventionally, seismic attributes derived from migrated reflections are used for this purpose. The attributes derived from the other counterparts of the recorded wavefield are often ignored and excluded from the categorization. We have performed categorization of the attributes derived from the diffracted part of the wavefield and combine them into a new seismic attribute class, which we call diffractivity attributes. The extraction of diffractivity attributes is based on the 3D Kirchhoff time migration operator that includes a dynamic muting. We distinguish three major classes in the diffractivity attributes, which describe geometric and amplitude properties of the seismic diffractions. We assign point and edge diffraction focusing as well as the azimuth to the geometric class. The amplitudes of the isolated seismic diffractions are used to extract the instantaneous attributes based on the complex-trace approach. The instantaneous amplitudes, phase, frequency, and sweetness build up the instantaneous attribute class. We perform a spectral decomposition of the isolated diffractions into the isofrequencies using the wavelet approach. The isofrequencies compose the spectral-decomposition class. We also link the new diffractivity class to the conventional seismic reflection attributes. We use a deep learning approach based on convolutional neural networks for classifying and correlating the diffractivity attributes.