  We examine the hydrodynamics of systems with spontaneously broken multipolar
symmetries using a systematic effective field theory. We focus on the simplest
non-trivial setting: a system with charge and dipole symmetry, but without
momentum conservation. When no symmetries are broken, our formalism reproduces
the quartic subdiffusion ($\omega \sim -i k^4$) characteristic of `fracton
hydrodynamics' with conserved dipole moment. Our formalism also captures
spontaneous breaking of charge and/or dipole symmetry. When charge symmetry is
spontaneously broken, the hydrodynamic modes are quadratically propagating and
quartically relaxing ($\omega \sim \pm k^2 - ik^4$). When the dipole symmetry
is spontaneously broken but the charge symmetry is preserved, then we find
quadratically relaxing (diffusive) transverse modes, plus another mode which
depending on parameters may be either purely diffusive ($\omega \sim -i k^2$)
or quadratically propagating and quadratically relaxing ($\omega \sim \pm k^2
-i k^2$). Our work provides concrete predictions that may be tested in
near-term cold atom experiments, and also lays out a general framework that may
be applied to study systems with spontaneously broken multipolar symmetries.
