We show theoretically that an imposed uniaxial anisotropy leads to new universality classes for the dynamics of active particles suspended in a viscous fluid. In the homogeneous state, their concentration relaxes superdiffusively, stirred by the long-ranged flows generated by its own fluctuations, as confirmed by our numerical simulations. Increasing activity leads to an anisotropic diffusive instability, and thus an original phase-separation mechanism, driven by the interplay of active stresses with a particle current proportional to the local curvature of the suspension velocity profile.

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• Self-propelled particles
• Suspensions
• Theories of collective dynamics & active matter