Subsurface fluid injection is often followed by observations of an enlarging cloud of microseismicity. The cloud’s diffusive growth is thought to be a direct response to the diffusion of elevated pore fluid pressure reaching pre-stressed faults, triggering small instabilities; the observed high rates of this growth are interpreted to reflect a relatively high permeability of a fractured subsurface [e.g., Shapiro, GJI 1997]. We investigate an alternative mechanism for growing a microseismic cloud: the elastic transfer of stress due to slow, aseismic slip on a subset of the pre-existing faults in this damaged subsurface. We show that the growth of the slipping region of the fault may be self-similar in a diffusive manner. While this slip is driven by fluid injection, we show that, for critically stressed faults, the apparent diffusion of this slow slip may quickly exceed the poroelastically driven diffusion of the elevated pore fluid pressure. We also examine recent field injection experiments providing time series, measured at the borehole, of both fluid pressure as well as the relative displacement of a fault cross-cutting the borehole [Guglielmi et al., 2015]. We couple a hydrogeologic model for fluid flow from the borehole with a model for an expanding shear rupture of the fault. We find that such a model reproduces the observed time history, with a Bayesian inversion providing uncertainties of the model parameters for host rock stiffness and frictional strength, fault zone storage and permeability, as well as the pre-injection stress state. Remarkably, we also find that the inferred rupture front outpaces the region of significant pore pressure increase.