The Transiting Exoplanet Survey Satellite (TESS) is providing precise time-series photometry for most star clusters in the solar neighborhood. Using the TESS images, we have begun a Cluster Difference Imaging Photometric Survey (CDIPS), in which we are focusing both on stars that are candidate cluster members, and on stars that show indications of youth. Our aims are to discover giant transiting planets with known ages, and to provide light curves suitable for studies in stellar astrophysics. For this work, we made 159,343 light curves of candidate young stars, across 596 distinct clusters. Each light curve represents between 20 and 25 days of observations of a star brighter than $G_{rm Rp}=16$, with 30-minute sampling. We describe the image subtraction and time-series analysis techniques we used to create the light curves, which have noise properties that agree with theoretical expectations. We also comment on the possible utility of the light curve sample for studies of stellar rotation evolution, and binary eccentricity damping. The light curves, which cover about one sixth of the galactic plane, are available as a MAST High Level Science Product at https://doi.org/10.17909/t9-ayd0-k727 .
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