Abstract—Heterogeneous cellular networks (HCNs) with em-bedded small cells are considered, where multiple mobile users wish to download network content of different popularity. By caching data into the small-cell base stations, we will design distributed caching optimization algorithms via belief propagation (BP) for minimizing the downloading latency. First, we derive the delay-minimization objective function and formulate an opti-mization problem. Then, we develop a framework for modeling the underlying HCN topology with the aid of a factor graph. Furthermore, a distributed BP algorithm is proposed based on the network’s factor graph. Next, we prove that a fixed point of convergence exists for our distributed BP algorithm. In order to reduce the complexity of the BP, we propose a heuristic BP algorithm. Furthermore, we evaluate the average downloading performance of our HCN for different numbers and locations