Cellular decision making is accomplished by complex networks, the structure of which has traditionally been inferred from mean gene expression data. In addition to mean data, detailed quantitative measures of distributions across a population can be obtained using techniques such as flow cytometry that measure expression in single cells. The resulting distributions, which reflect a population's variability or noise, constitute a potentially rich source of information for network reconstruction. A significant portion of molecular noise in a biological process is propagated from the upstream regulators. This propagated component provides additional information about causal network connections. Here, we devise a procedure in which we exploit equations for dynamic noise propagation in a network under non-steady state conditions to distinguish between alternate regulatory relationships in a network. We test our approach in silico using data obtained from stochastic simulations as well as in vivo using experimental data collected from synthetic circuits constructed in yeast.