(From Wikipedia) predictive processing (a.k.a. predictive coding, the Bayesian Brain hypothesis) is a theory of brain function in which the brain is constantly generating and updating a mental (generative) model of the environment. The model is used to generate predictions of sensory input that are compared to actual sensory input. This comparison results in prediction errors that are then used to update and revise the mental model.

Active Inference (AIF) can be seen as a generalization of predictive processing. While predictive processing only explains the agent's perception in terms of inference, AIF models both perception and action as inference under closely related objectives: whereas perception minimizes variational free energy (which sometimes reduces to precision-weighted prediction error), action minimizes expected free energy.

The Free Energy Principle is a generalization of AIF that not only attempts to describe biological organisms, but rather all systems that maintain a separation from their environments (via Markov blankets).

External Links:
Book Review: Surfing Uncertainty - Introduction to predictive processing by Scott Alexander
Predictive Processing And Perceptual Control by Scott Alexander
Predictive coding under the free-energy principle by Karl Friston and Stefan Kiebel

Related Pages: Perceptual Control Theory, Neuroscience, Free Energy Principle