We study a continuum model of overdamped self-propelled particles with aligning interactions in two dimensions. Combining analytical theory and computations, we map out the phase diagram for the parameter space covered by the model. We find that the system self-organizes into two robust structures in different regions of parameter space: solitary waves composed of ordered swarms moving through a low density disordered background, and stationary radially symmetric asters. The self-regulating nature of the flow yields phase separation, ubiquitous in this class of systems, and controls the formation of solitary waves. Self-propulsion and the associated active convection play a crucial role in aster formation.