We present a model for explaining the seismicity rate of fluid-injection-induced earthquakes. It is assumed that pore-pressure diffusion is the main triggering mechanism, and that the criticality of the medium is randomly distributed. Based on these and other poroelastic and stochastic assumptions, we derive equations for the induced seismicity rate during and after fluid injection. On this basis, a method is proposed for estimating hydraulic diffusivity using only the observed seismicity rate and an estimate of the activated seismogenic volume. This approach differs from previous methods in that an accurate hypocentral parameter catalog is not required. Numerical investigation of the proposed method indicates that it is relatively robust with respect to the activated seismogenic volume dimension estimate. Application of the technique to two Hot Dry Rock experiments, Fenton Hill and Soultz, produces diffusivity values that are consistent with independent estimates from prior investigations.