  Interfaces of phase-separated systems roughen in time due to capillary waves.
Because of fluxes in the bulk, their dynamics is nonlocal in real space and is
not described by the Edwards-Wilkinson or Kardar-Parisi-Zhang (KPZ) equations,
nor their conserved counterparts. We show that in the absence of detailed
balance, the phase-separated interface is described by a new universality class
that we term |q|KPZ. We compute the associated critical exponents via one-loop
renormalization group, and corroborate the results by numerical integration of
the |q|KPZ equation. Deriving the effective interface dynamics from a minimal
field theory of active phase separation, we finally argue that the |q|KPZ
universality class generically describes liquid-vapor interfaces in active
systems.
