In many subduction zones, the plate interface hosts intermittent, low-frequency, low-magnitude seismic tremor and low-frequency earthquakes (LFEs). Seismic activity clusters in episodic bursts that migrate along the fault zone in complex ways. Geological structures in fossil tremor source regions testify to large and pervasive variations of fluid pressure and permeability. Here, we explore the potential of fluid pressure transients in a permeable subduction interface to trigger seismic sources and induce interactions between them. We show how variations of pore pressure and permeability can act in tandem to generate tremor-like patterns. The core feature of the model is that lowpermeability plugs behave as elementary fault-valves. In a mechanism akin to erosive bursts and deposition events documented in porous media, valve permeability opens and closes in response to the local fluid pressure distribution. The rapid pressure release and/or mechanical fracturing associated with valve opening acts as the source of an LFE-like event. Valves interact constructively, leading to realistic, tremor-like patterns: cascades, synchronized bursts and migrations of activity along the channel, on both short and long time and space scales. Our model predicts that the input fluid flux is a key control on activity occurrence and behavior. Depending on its value, the subduction interface can be seismically quiescent or active, and seismicity can be strongly time-clustered, quasi-periodic or almost random in time. This model allows new interpretations of low frequency seismic activity in terms of effective fluid flux and fault-zone permeability.