From August 2018 to May 2019, Kīlauea’s summit exhibited unique, simultaneous, inflation and deflation, apparent in both GPS time series and cumulative InSAR displacement maps. This deformation pattern provides clear evidence that the Halema‘uma‘u (HMM) and South Caldera (SC) reservoirs are distinct. Post-collapse inflation of the East Rift Zone (ERZ), as captured by InSAR, indicates concurrent magma transfer from the summit reservoirs to the ERZ. We present a physics-based model that couples pressure-driven flow between these magma reservoirs to simulate time dependent summit deformation. We take a two-step approach to quantitatively constrain Kīlauea’s magmatic plumbing system. First, we jointly invert the InSAR displacement maps and GPS offsets for the location and geometry of the summit reservoirs, approximated as spheroidal chambers. We find that HMM reservoir has an aspect ratio of ~1.8 (prolate) and a depth of ~2.2 km (below surface). The SC reservoir has an aspect ratio of ~0.14 (oblate) and a depth of ~3.6 km. Second, we utilize the flux model to invert GPS time series from 8 summit stations. Results favor a shallow HMM-ERZ pathway an order of magnitude more hydraulically conductive than the deep SC-ERZ pathway. Further analysis shows that the HMM-ERZ pathway is required to explain the deformation time series. Given high-quality geodetic data, such an approach promises to quantify the connectivity of magmatic pathways between reservoirs in other similar volcanic systems.