A novel computational treatment of dense, stiff, coupled reaction rate equations is introduced to study the nucleation, growth, and possible coalescence of cavities during neutron irradiation of metals. Radiation damage is modeled by the creation of Frenkel pair defects and helium impurity atoms. A multi-dimensional cluster size distribution function allows independent evolution of the vacancy and helium content of cavities, distinguishing voids and bubbles. A model with sessile cavities and no cluster-cluster coalescence can result in a bimodal final cavity size distribution with coexistence of small, high-pressure bubbles and large, low-pressure voids. A model that includes unhindered cavity diffusion and coalescence ultimately removes the small helium bubbles from the system, leaving only large voids. The terminal void density is also reduced and the incubation period and terminal swelling rate can be greatly altered by cavity coalescence. Temperature-dependent trapping of voids/bubbles by precipitates and alterations in void surface diffusion from adsorbed impurities and internal gas pressure may give rise to intermediate swelling behavior through their effects on cavity mobility and coalescence.