We evaluate an ambient, bidirectional thermal network, which uses a single circuit for both district heating and cooling. When in net more cooling is needed than heating, the system circulates from a central plant in one direction. When more heating is needed, the system circulates in the opposite direction. A large benefit of this design is that buildings can recover waste heat from each other directly. We analyze the thermodynamic performance of the bidirectional system. Because the bidirectional system represents the state-of-the-art in design for district systems, its peak energy efficiency represents an upper bound on the thermal performance of any district heating and cooling system. However, because any network has mechanical and thermal distribution losses, we develop a diversity criterion to understand when the bidirectional system may be a more energy-efficient alternative to modern individual-building systems. We show that a simple model of a low-density, high-distribution loss network is more efficient than aggregated individual buildings if there is at least 1 unit of cooling energy per 5.7 units of simultaneous heating energy (or vice versa). We apply this criterion to reference building profiles in three cities to look for promising clusters.