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The inventory and variability of oceanic dissolved inorganic carbon (DIC) is driven by the interplay of physical, chemical, and biological processes. Quantifying the spatiotemporal variability of these drivers is crucial for a mechanistic understanding of the ocean carbon sink and its future trajectory. Here, we use the Estimating the Circulation and Climate of the Ocean-Darwin ocean biogeochemistry state estimate to generate a global-ocean, data-constrained DIC budget and investigate how spatial and seasonal-to-interannual variability in three-dimensional circulation, air-sea CO2 flux, and biological processes have modulated the ocean sink for 1995-2018. Our results demonstrate substantial compensation between budget terms, resulting in distinct upper-ocean carbon regimes. For example, boundary current regions have strong contributions from vertical diffusion while equatorial regions exhibit compensation between upwelling and biological processes. When integrated across the full ocean depth, the 24-year DIC mass increase of 64 Pg C (2.7 Pg C year-1) primarily tracks the anthropogenic CO2 growth rate, with biological processes providing a small contribution of 2% (1.4 Pg C). In the upper 100 m, which stores roughly 13% (8.1 Pg C) of the global increase, we find that circulation provides the largest DIC gain (6.3 Pg C year-1) and biological processes are the largest loss (8.6 Pg C year-1). Interannual variability is dominated by vertical advection in equatorial regions, with the 1997-1998 El Niño-Southern Oscillation causing the largest year-to-year change in upper-ocean DIC (2.1 Pg C). Our results provide a novel, data-constrained framework for an improved mechanistic understanding of natural and anthropogenic perturbations to the ocean sink.