The decay of organic matter in natural ecosystems is controlled by a network of biologically, physically, and chemically driven processes. Decomposing organic matter is often described as a continuum that transforms and degrades over a wide range of rates, but it is difficult to quantify this heterogeneity in models. Most models of carbon degradation consider a network of only a few organic matter states that transform homogeneously at a single rate. These models may fail to capture the range of residence times of carbon in the soil organic matter continuum. Here we assume that organic matter is distributed among a continuous network of states that transform with stochastic, heterogeneous kinetics. We pose and solve an inverse problem in order to identify the rates of carbon exiting the underlying degradation network (exit rates) and apply this approach to plant matter decay throughout North America. This approach provides estimates of carbon retention in the network without knowing the details of underlying state transformations. We find that the exit rates are approximately lognormal, suggesting that carbon flow through a complex degradation network can be described with just a few parameters. These results indicate that the serial and feedback processes in natural degradation networks can be well approximated by a continuum of parallel decay rates.