Free association among words is a fundamental and ubiquitous memory task. Although distributed semantics (DS) models can predict the association between pairs of words, and semantic network (SN) models can describe transition probabilities in free association data, there have been few attempts to apply established cognitive process models of memory search to free association data. Thus, researchers are currently unable to explain the dynamics of free association using memory mechanisms known to be at play in other retrieval tasks, such as free recall from lists. We address this issue using a popular neural network model of free recall, the context maintenance and retrieval (CMR) model, which we fit using stochastic gradient descent on a large data set of free association norms. Special cases of CMR mimic existing DS and SN models of free association, and we find that CMR outperforms these models on out-of-sample free association data. We also show that training CMR on free association data generates improved predictions for free recall from lists, demonstrating the value of free association for the study of many different types of memory phenomena. Overall, our analysis provides a new account of the dynamics of free association, predicts free association with increased accuracy, integrates theories of free association with established models of memory, and shows how large data sets and neural network training methods can be used to model complex cognitive processes that operate over thousands of representations.