Large bathymetric gradients associated with volcanic seamounts can drive convective flow, while thick sedimentary aprons that typically surround volcanic edifices host compaction-driven flow. In these submarine environments the interactions of compaction-driven and buoyancy-driven fluid flow lead to complex hydrogeologic regimes. We apply transient numerical models of coupled fluid flow and heat transport to the Hawaiian, Canary, and Marquesas Islands to examine the role of volcanic architecture on the evolution of fluid flow and pore pressure during volcanic building, lithospheric flexure, sedimentation, and compaction. The islands differ in edifice size, sedimentary apron structure, amount of lithospheric flexure, and sedimentation and volcanic growth rates. By comparing these variations, we examine how geometry and geologic history affect fluid flow and pore pressure patterns. Buoyancy-driven flow is most influenced by edifice height and amount of lithospheric flexure. Compaction-driven flow is altered primarily by thickness of prevolcanic sediment, the sedimentation rate, and the size of the volcanic edifice. In Hawaii, the area with the highest edifice and most flexure, flow velocities and excess pore pressures are greatest, with Darcy velocities of >30 mm/yr and excess pressures of >7 MPa during the beginning of volcanic building. High sedimentation rates in the Marquesas sedimentary apron increase fluid velocities in the later portion of volcanic building, with Darcy velocities >12 mm/yr. In the Canary Islands, compaction-driven flow occurs for an extended time period because of long, slower volcanic building, resulting in Darcy velocities >10 mm/yr that endure over 5 Myr.