Seismic diffraction waveform energy contains important information about small-scale subsurface elements, and it is complementary to specular reflection information about subsurface properties. Diffraction imaging has been used for fault, pinchout, and fracture detection. Very little research, however, has been carried out taking diffraction into account in the impedance inversion. Usually, in the standard inversion scheme, the input is the migrated data and the assumption is taken that the diffraction energy is optimally focused. This assumption is true only for a perfectly known velocity model and accurate true amplitude migration algorithm, which are rare in practice. We have developed a new approach for impedance inversion, which takes into account diffractive components of the total wavefield and uses the unmigrated input data. Forward modeling, designed for impedance inversion, includes the classical specular reflection plus asymptotic diffraction modeling schemes. The output model is composed of impedance perturbation and the low-frequency model. The impedance perturbation is estimated using the Bayesian approach and remapped to the migrated domain by the kinematic ray tracing. Our method is demonstrated using synthetic and field data in comparison with the standard inversion. Results indicate that inversion with taking into account diffraction can improve the acoustic impedance prediction in the vicinity of local reflector discontinuities.