Passive degassing, or volatile release from persistent, non-eruptive volcanic activity, may have contributed significantly to the Martian ice budget over the planet's history by providing a pathway for volatile species, such as water vapor, to outgas from the interior into the atmosphere and accumulate on the surface. Passive degassing from Martian volcanoes can result in ice accumulations in unusual locations (e.g., outside of the typical cold traps like the Tharsis Rise and polar ice caps). Such locally derived water could cover the volcanic source in an ice-rich veneer that may later serve as a source of ice for subsequent interactions between impactors or lava. Using the Laboratoire de Météorologie Dynamique Generic Planetary Climate Model, we model the spatial distribution of ice that results from passive degassing from five major Martian volcanic centers, Cerberus Fossae, Apollinaris Mons, Elysium Mons, Hadriacus Mons, and Pityusa Patera, and assess the sensitivity of these results to a range of volcanic, atmospheric, orbital, environmental, and numerical parameters. Previous studies have placed estimates on the amount of water released from volcanic outgassing (e.g., Carr, 1987; Craddock and Greeley, 2009; Grott et al., 2011; Carr and Head, 2015), but this is the first study to track the water released from specific volcanoes and to determine the spatial distribution of resulting ice deposits. We find that volcanic variables, such as mass flux and duration of degassing, primarily drive the thickness of volcanogenic ice fields –– higher mass fluxes create the thickest ice deposits (up to ∼210 mm around the volcanic center for a mass flux 106 kg s−1) and durations of >6 months are required for ice to reach near-global distributions. Ice accumulation around the degassing source is maximized if the latitude of passive degassing occurs near the south pole (i.e., Pityusa Patera) due to its exposure to circulation patterns that promote ice deposition in that region. Changes in the season, dust visible optical depth, and eccentricity can also impact the thickness of ice, with ice accumulation around the volcanic source being maximized in the spring, with higher dust visible optical depths, and when the eccentricity is low, due to more favorable temperatures and atmospheric circulation. Variances in the obliquity can also influence ice fields by modulating which latitudes receive more surface ice accumulation. The amount of activated cloud condensation nuclei (CCN) in the atmosphere has a lesser impact on the thickness and spatial distribution of ice fields than other parameters, with lower amounts of CCN leading to narrower, but slightly thicker deposits compared to higher amounts of CCN. The mean surface pressure and longitude of perihelion both affect the timing of ice fields. The surface pressure influences how long water lingers in the atmosphere before depositing to the surface, while the longitude of perihelion controls the time of year in which the thickest ice deposits accumulate around the degassing source. Ice fields are highly sensitive to the model resolution. Higher model resolutions allow for a more detailed representation of physical processes, such as cloud formation and ice deposition, while lower resolution model runs provide a more approximate guide to the representation of these processes and may underestimate surface ice thicknesses around the degassing source. The thickest deposits of ice form around the source of passive degassing, but later migrates and restabilizes in cold traps after degassing has ceased, unless it is protected against sublimation by the deposition of dust or pyroclastic material. Assuming the ice is protected, recurrent episodes of passive degassing could have facilitated the gradual accumulation of ice deposits several meters thick over time.