The 2004–2009 caldera uplift is the largest instrumentally recorded episode of unrest at Yellowstone caldera. We use GPS and Interferometric Synthetic Aperture Radar (InSAR) time series spanning 2004–2015, with a focus in the aforementioned event to understand the mechanisms of unrest. InSAR data recorded ∼25 and ∼20 cm of uplift at the Sour Creek (SCD) and Mallard Lake (MLD) resurgent domes during 2004–2009, and ∼8 cm of subsidence at the Norris Geyser Basin (NGB) during 2004–2008. The SCD/MLD uplift was followed by subsidence across the caldera floor with a maximum at MLD of ∼1.5–2.5 cm/yr, and no deformation at NGB. The best-fit source models for the 2004–2009 period are two horizontal sills at depths of ∼8.7 and 10.6 km for the caldera source and NGB, respectively, with volume changes of 0.354 and −0.121 km3, and an overpressure of ∼0.1 MPa. The InSAR and GPS time series record exponentially increasing followed by exponentially decreasing uplift between 2004 and 2009, which is indicative of magma injection into the caldera reservoir, with no need for other mechanisms of unrest. However, magma extraction from NGB to the caldera is unable to explain the subsidence coeval with the caldera uplift. Models of magma injection can also explain other episodes of caldera uplift like that in 2014–2015. Distributed sill opening models show that magma is stored across the caldera source with no clear boundary between MLD and SCD. Since the magma overpressure is orders of magnitude below the tensile strength of the encasing rock, historical episodes of unrest like these are very unlikely to trigger an eruption.