AbstractFluid‐induced earthquake sequences generally appear as expanding swarms activating a particular fault. The recent analysis of a swarm in the Corinth rift has revealed a dual migration pattern, with a global slow expansion (m day−1) and episodes of rapid migration (km day−1). Such swarms are generally interpreted as fluid diffusion, which ignores the possibility of static, dynamic, or aseismic triggering and the existence of rapid migration. Here, we propose a new model for such swarms, where earthquakes consist in the failure of asperities on a creeping fault infiltrated by fluid. For that, we couple rate‐and‐state friction, nonlinear diffusivity, and elasticity along a 1D interface. This model reproduces the dual migration speeds observed in real swarms. We show that migration speeds increase linearly with the mean pressurization and are not dependent on the hydraulic diffusivity, as traditionally suggested.