A key insight from Bayesian machine learning is that adaptive learning requires distinguishing between two types of noise: speed of change or volatility and moment-to-moment stochasticity. Although this is a computationally difficult problem, the brain can solve it; the question is, how? We addressed this issue by developing a model that learns to distinguish between volatility and stochasticity solely through observations over time. The model has two modules: a stochasticity module and a volatility module. These modules must compete within the model to explain experienced noise. This enables us to explain aspects of human and animal data across a wide range of seemingly unrelated neuroscientific and behavioral phenomena. It also provides a rich set of hypotheses about pathological learning in psychiatric conditions, where damage in one module impacts the behavior with regard to the other factor because the model misattributes all noise to the remaining module.