The diffuse scattering from crystals containing defect clusters with strong displacement fields has been calculated. The scattering is extremely large and concentrated in small regions near the Bragg reflections. For small concentrations the diffuse intensity is essentially determined by a "cluster form factor" depending explicitly on the displacement field. The scattering is studied in detail for small and large deviations from the Bragg reflection. Exact expressions are given for the moments of the scattering, depending sensitively on the displacement field in the core of the cluster. The diffuse scattering for strong displacement fields shows a pronounced asymmetry; its center does not coincide with the position of the Bragg peak, in agreement with recent experimental observations.