  Active Inference (AIF) is an emerging framework in the brain sciences which
suggests that biological agents act to minimise a variational bound on model
evidence. Control-as-Inference (CAI) is a framework within reinforcement
learning which casts decision making as a variational inference problem. While
these frameworks both consider action selection through the lens of variational
inference, their relationship remains unclear. Here, we provide a formal
comparison between them and demonstrate that the primary difference arises from
how value is incorporated into their respective generative models. In the
context of this comparison, we highlight several ways in which these frameworks
can inform one another.
