We analyze frontal dynamics of dilute powder snow avalanches sustained by rapid blow-out behind the front. Such material injection arises as a weakly cohesive snow cover is fluidized by the very pore pressure gradient that the particle cloud induces within the snowpack. We model cloud fluid mechanics as a potential flow consisting of a traveling source of denser fluid thrust into a uniform airflow. Stability analysis of a mass balance involving snow cover and powder cloud yields relations among scouring depth, frontal height, speed, mixed-mean density, and impact pressure when the frontal region achieves a stable growth rate. We compare predictions with field measurements, show that powder clouds cannot reach steady frontal speed on a uniform snowpack with constant cloud width and derive a criterion for cloud ignition. Because static pressure is continuous across the mean air-cloud interface and deviatoric stresses are negligible, frontal acceleration is insensitive to local slope, but instead arises from a deficit of flow-induced suction in the wake. We calculate how far a powder cloud travels until its frontal mixed-mean density becomes stable, and show how topographic spread can hasten its collapse.