It is widely recognized that fluid injection can trigger fault slip. However, the processes by which the fluid-rock interactions facilitate or inhibit slip are poorly understood and some are neglected or oversimplified in most models of injection-induced slip. In this study, we perform a 2D antiplane shear investigation of aseismic slip that occurs in response to fluid injection into a permeable fault governed by rate-and-state friction. We account for pore dilatancy and permeability changes that accompany slip, and quantify how these processes affect pore pressure diffusion, which couples to aseismic slip. The fault response to injection has two phases. In the first phase, slip is negligible and pore pressure closely follows the standard linear diffusion model. Pressurization of the fault eventually triggers aseismic slip in the immediate vicinity of the injection site. In the second phase, the aseismic slip front expands outward and dilatancy causes pore pressure to depart from the linear diffusion model. Aseismic slip front overtakes pore pressure contours, with both subsequently advancing at constant rate along fault. We quantify how prestress, initial state variable, injection rate, and frictional properties affect the migration rate of the aseismic slip front, finding values ranging from less than 50 to 1000 m/day for typical parameters. Additionally, we compare to the case when porosity and permeability evolution are neglected. In this case, the aseismic slip front migration rate and total slip are much higher. Our modeling demonstrates that porosity and permeability evolution, especially dilatancy, fundamentally alters how faults respond to fluid injection.