A fundamental precondition for the secure and efficient operation of district heating networks (DHNs) is a stable hydraulic behavior. However, the ongoing transition towards a sustainable heat supply, especially the rising integration of distributed heat sources and the increasingly meshed topologies, introduce complex and potentially destabilizing hydraulic dynamics. In this work, we propose a unifying, passivity-based framework which guarantees asymptotic stability of any forced hydraulic DHN equilibrium while allowing for meshed, timevarying topologies and different, dynamically interacting distributed heat sources. To establish the desired hydraulic equilibria, we propose decentralized, passivity-based pressure and volume flow rate controllers for the pumps and valves in the actuated DHN subsystems. In particular, we leverage the equilibriumindependent passivity (EIP) properties of the DHN subsystems, the skew-symmetric nature of their interconnections, and LaSalle's Invariance principle to assess asymptotic stability in a modular manner. The obtained results hold for the state-of-theart as well as future DHN generations featuring, for example, multiple distributed heat sources, asymmetric pipe networks, and multiple temperature layers. We verify our findings by means of simulations. * * F. Strehle and J. Machado contributed equally.* * * The work of J.