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Abstract Enigmatic large‐scale (>150 km wide) ground deformation in southern Bolivia has been ongoing for more than 50 year. Concurrent changes in gravity recorded between 2010 and 2018 imply minor changes in subsurface density in the absence of significant mass changes. Numerical modeling of the gravity changes and concurrent InSAR LOS displacements gives annual bulk density changes of 0.002 kg m⁻³in the Altiplano‐Puna Magma Body (APMB) and −0.03 kg m⁻³in a vertical bulge‐column ensemble beneath Uturuncu volcano. We propose that the transcrustal migration of fluids from the APMB to shallower crustal levels by compressible flow is the source of ground deformation. Localized ground subsidence south of Uturuncu can be best explained by a density decrease of 20 ± 5 kg m⁻³between 2011 and 2013 in a hydrothermal reservoir. Our findings contribute to the growing recognition of transcrustal fluid migration as a source of volcanic unrest.