Multiple neural and synaptic phenomena take place in the brain. They operate over a broad range of timescales, and the consequences of their interplay are still unclear. In this work, I study a computational model of a recurrent neural network in which two dynamic processes take place: sensory adaptation and synaptic plasticity. Both phenomena are ubiquitous in the brain, but their dynamic interplay has not been investigated. I show that when both processes are included, the neural circuit is able to perform a specific computation: it becomes a generative model for certain distributions of input stimuli. The neural circuit is able to generate spontaneous patterns of activity that reproduce exactly the probability distribution of experienced stimuli. In particular, the landscape of the phase space includes a large number of stable states (attractors) that sample precisely this prior distribution. This work demonstrates that the interplay between distinct dynamical processes gives rise to useful computation, and proposes a framework in which neural circuit models for Bayesian inference may be developed in the future.