We discuss a connection between spatial branching processes and the PHD recursion based on conditioning principles for Poisson Point Processes. The branching process formulation gives a generalized Feynman-Kac systems interpretation of the PHD filtering equations, which enables the derivation of mean-field implementations of the PHD filter. This approach provides a principled means for obtaining target tracks and alleviates the need for pruning, merging and clustering for the estimation of multi-target states.