A mechanism for compiling a generative description of an inference task into a neural network. First, an arbitrary generative probabilistic model from the exponential family is specified (or received). The model characterizes a conditional probability distribution for measurement data given a set of latent variables. A factor graph is generated for the generative probabilistic model. Each factor node of the factor graph is expanded into a corresponding sequence of arithmetic operations, based on a specified inference task and a kind of message passing algorithm. The factor graph and the sequences of arithmetic operations specify the structure of a neural network for performance of the inference task. A learning algorithm is executed, to determine values of parameters of the neural network. The neural network is then ready for performing inference on operational measurements.