Detecting surface deformation associated with low-magnitude (Mw ≤ 5) seismicity using interferometric synthetic aperture radar (InSAR) is challenging due to the subtlety of the signal and the often challenging imaging environments. However, low-magnitude earthquakes are potential precursors to larger seismic events, and thus characterizing the crustal displacement associated with them is crucial for regional seismic hazard assessment. We combine InSAR time-series techniques with a Deep Learning (DL) autoencoder denoiser to detect the magnitude and extent of crustal deformation from the Mw = 3.4 Gallina, New Mexico earthquake that occurred on 30 July 2020. Although InSAR alone cannot detect event-related deformation from such a low-magnitude seismic event, application of the DL method reveals maximum displacements as small as (±2.5 mm) in the vicinity of both the fault and earthquake epicenter without prior knowledge of the fault system. This finding improves small-scale displacement discernment with InSAR by an order of magnitude relative to previous studies. We additionally estimate best-fitting fault parameters associated with the observed deformation. The application of the DL technique unlocks the potential for low-magnitude earthquake studies, providing new insights into local fault geometries and potential risks from higher-magnitude earthquakes. This technique also permits low-magnitude event monitoring in areas where seismic networks are sparse, allowing for the possibility of global fault deformation monitoring.