Using a hierarchy of models, we develop a theoretical framework for understanding the physical processes controlling the magnitude and patterns of the saturation state of dissolved argon (δAr) in the ocean. A conceptual box model of the argon cycle demonstrates that the saturation state of argon in the thermocline can be considered a linear combination of a preformed disequilibrium (δArpre) governed by surface processes and mapped into the ocean interior, and a supersaturation driven by diapycnal mixing in the interior ocean (δArmix). The magnitude of δArmix is determined by the relative strength of isopycnal ventilation and diapycnal mixing in the thermocline. We extend the simple theory to a three-dimensional, continuously stratified ocean by deriving a mathematical relationship between diapycnal mixing, air-sea heat fluxes and the saturation state of argon. This relationship predicts that the δAr of a water parcel increases following its flow path at a rate that is proportional to the diapycnal diffusivity ($kappa$). The theoretical predictions are evaluated with a numerical ocean basin model showing reasonable agreement between simulated argon distribution and the theory. We find three distinctive regimes in which different dynamical balances determine the saturation state of argon in the thermocline. First, newly ventilated water in the subtropical gyre is dominated by δArpre, reflecting the balance between air-sea heat transfer and the gas exchange rates. Second, the saturation state of argon in the tropical thermocline is primarily determined by δArmix, reflecting the important roles of diapycnal mixing there. Third, at the transition between the ventilated gyre and the poorly ventilated tropics, δArpre and δArmix together control the saturation state of argon. In this region, δAr is sensitive to model diffusivity, which can be estimated from the simulated distribution of δAr with an error of less than 50%. Thus noble gas concentrations may provide a unique constraint on the basin-scale diapycnal diffusivity of the subtropical thermocline.