A model of an associative neural network is developed in which the state of each node is described by a probability density. The realization of the network is based on the pairwise joint probabilities obtained from a training set of states. A positive definite ‘‘energy’’ functional of the probabilities may be constructed from Bayes’ rule of statistical inference. When the states of some of the nodes are fixed as constraints, the minimization of the energy yields a set of probability functions which is consistent with the original pairwise correlations.