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Stellar activity interferes with precise radial velocity measurements and limits our ability to detect and characterize planets, in particular Earth-like planets. We introduce AESTRA (Auto-Encoding STellar Radial-velocity and Activity), a deep-learning method for precise radial velocity measurements. It combines a spectrum autoencoder, which learns to create realistic models of the star’s rest-frame spectrum, and a radial-velocity estimator, which learns to identify true Doppler shifts in the presence of spurious shifts due to line-profile variations. Being self-supervised, AESTRA does not need “ground truth” radial velocities for training, making it applicable to exoplanet host stars for which the truth is unknown. In tests involving 1000 simulated spectra, AESTRA can detect planetary signals as low as 0.1 m s ^−1 even in the presence of 3 m s ^−1 of activity-induced noise and 0.3 m s ^−1 of photon noise per spectrum.