Perception consists of two parts
In order to learn the the generative model $p_\theta(x,z)$, the Free energy principle suggest to maximize the evidence of an observation $x$ using gradient ascent. The evidence is given by $\ln p_\theta(x)$. The gradient of the evidence w.r.t. $\theta$ is given by
\[\frac{\partial}{\partial\theta} p_\theta(x) = \sum_z p_\theta(z\mid x) \frac{\partial}{\partial\theta}\ln p_\theta(x,z).\]Note that in order to compute this gradient we need to have access to $p_\theta(z\mid x)$. In the next section we discuss how this can be approximated.
Assume that we have a model $p_\theta(x \mid z)$ of how the world is generating observations $x$ from latent causes $z$, and we have a prior distribution $p_\theta(z)$ over latent causes. Given a specific observation $x$, the goal of inference is to find the posterior distribution $p_\theta(z \mid x)$. Computing this distribution exactly is often hard. The Free energy principle suggest to find an approximate posterior $q_x(z)$ in a family of distributions $\cQ$ that minimises the following free energy function w.r.t. $q$:
\[F(p,q,x) = \sum_z q(z) \ln\frac{q(z)}{p_\theta(x,z)}.\]Thus,
\[q_x(z) = \argmin_{q \in \cQ} F(p,q,x).\]Note that when $\cQ$ is the set of all distributions over $z$, $q_x(z)$ will simply be equal to $p_\theta(z\mid x)$. Usually, however, $\cQ$ does not contain all probability distributions, and is parametrized by a parameter $\phi$.