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.