AbstractInterferometric synthetic aperture radar (InSAR) has become an essential technique to detect surface variations due to volcanoes, earthquakes, landslides, glaciers, and aquifers. However, Earth's ionosphere, atmosphere, vegetation, surface runoff, etc., introduce noise that requires post‐processing to separate its components. This work defines a generator to create interferograms that include each of those components. Our approach leverages deformation models with real data, either directly or through machine learning using geostatistical methods. These methods result from previous developments to more efficiently and better simulate spatial variables and could replace some statistical approaches used in InSAR processing. We illustrate the use of the generator to simulate an artificial interferogram based on the 2015 Illapel earthquake and discuss the improved performance offered by geostatistical approaches compared with classical statistical ones. The generator establishes a tool for multiple applications (1) to evaluate InSAR correction workflows in controlled scenarios with known ground truth; (2) to develop training sets and generative methods for machine learning algorithms; and (3) to educate on InSAR and its principles.