The free-energy principle and active inference have received a significant attention in the fields of neuroscience and machine learning. However, it remains to be established whether active inference is an apt explanation for any given neural network that actively exchanges with its environment. To address this issue, we show that a class of canonical neural networks of rate coding models implicitly performs variational Bayesian inference under a well-known form of partially observed Markov decision process model (Isomura, Shimazaki, Friston, Commun Biol, 2022). Based on the proposed theory, we demonstrate that canonical neural networks—featuring delayed modulation of Hebbian plasticity—can perform planning and adaptive behavioural control in the Bayes optimal manner, through postdiction of their previous decisions. This scheme enables us to estimate implicit priors under which the agent’s neural network operates and identify a specific form of the generative model. The proposed equivalence is crucial for rendering brain activity explainable to better understand basic neuropsychology and psychiatric disorders. Moreover, this notion can dramatically reduce the complexity of designing self-learning neuromorphic hardware to perform various types of tasks.