  We investigate the coupled dynamics of charge and energy in interacting
lattice models with dipole conservation. We formulate a generic hydrodynamic
theory for this combination of fractonic constraints and numerically verify its
applicability to the late-time dynamics of a specific bosonic quantum system by
developing a microscopic non-equilibrium quantum field theory. Employing a
self-consistent $1/N$ approximation in the number of field components, we
extract all entries of a generalized diffusion matrix and determine their
dependence on microscopic model parameters. We discuss the relation of our
results to experiments in ultracold atom quantum simulators.
