The mineralogy of localized bright deposits on Ceres observed by the DAWN mission suggests their brine-enriched cryovolcanic origin. Based on the morphological observations of these deposits, explosive and effusive styles have been proposed for their eruption. Because volcanic eruption style and velocity are controlled by the extent of gas expansion inside the conduit, constraints on the internal aqueous environment, such as gas concentration and temperature, could be placed based on the observations of localized deposits on Ceres. However, the way these properties control the eruption style and velocity is complex. Cryomagma ascending from a subsurface reservoir gains buoyancy due to both boiling of water and exsolution of dissolved gas, owing to decompression to the extremely low pressure near the Ceres surface. Gas–melt segregation should also affect the dynamics. Thus, it is not yet fully understood how the internal environment of Ceres affects the ascent dynamics of cryovolcanism and subsequently controls the styles (explosive versus effusive) and velocities of eruptions. To address this problem, we developed a one-dimensional steady-state two-phase flow model for the ascent dynamics of gas-driven cryomagma under the conditions of Ceres taking both water boiling and gas exsolution into account. We found that the velocity and explosivity of an eruption are strongly controlled by the following three parameters, which characterize the cryomagmatic environment of Ceres's interior: (a) conduit conductivity (CC; rc2/μ, where rc is the conduit radius and μ is the magma viscosity), (b) dissolved gas concentration c0, and (c) magma reservoir temperature T0. Our model results reveal that low CC always leads to effusive or low-explosivity eruptions. Higher CC allows explosive eruption when either c0 or T0 is sufficiently high. These dependences can be summarized as four modes of eruption under the following CC-c0-T0 conditions. (1) Exsolution-driven explosive eruptions (X1 type) occur with volatile-rich magma (CC ≳ 10−3 m2/(Pa·s) and c0 ≳ 0.1 wt% of CO2). (2) Boiling-driven explosive eruptions (X2 type) occur with warm magma (CC ≳ 10−3 m2/(Pa·s), c0 ≪ 0.1 wt% of CO2, and high T0). (3) Viscosity-induced effusive eruptions (F1 type) occur with a narrow conduit and/or high-viscosity magma (CC ≲ 10−3 m2/(Pa·s)). (4) Low-gas-production-induced effusive eruptions (F2 type) occur with low-temperature and low-volatile magma (CC ≳ 10−3 m2/(Pa·s), c0 ≪ 0.1 wt% of CO2, and low T0). Our model predicts that either c0 ≳ 0.5 wt% of CO2 or T0 ≳−5°C is required for explosive eruptions to achieve eruption velocities ≳30 m/s, which has been proposed based on the size of some large faculae on Ceres. Such gas-rich or warm magma condition is unlikely to be achieved by equilibrium within the shallow crust. Thus, our results suggest that magma needs to be supplied from a deeper subsurface. In contrast, low-velocity effusion of brines has also been proposed based on morphometric analyses of evaporites on Ceres. Our results show that magma of such brine effusions is viscous and transported to the surface through a narrow conduit or they are sourced from reservoirs equilibrated to the ambient material within the shallow crust. Because the effusive eruption origin of faculae in the Occator crater is consistent with small conduits, the effusive nature may not necessarily rule out relatively high-volatile or warm magma inside Ceres in the recent past. These results show that the morphometric properties of facula deposits can place important constraints on the internal conditions of Ceres when the relevant eruption style/velocity is known. Our modeling results indicate that detailed observations (e.g., vesicularity, cooling history, and inclusion of eroded conduit material) of deposits and the possible vent structure in faculae by landing missions allow us to further probe the interior conditions of Ceres (e.g., magma temperature, gas concentration, viscosity, and conduit size).