Glow introduce

Let $X$ is a real high-dimensional random vector with unknown distribution, denoted as$X\sim p^{\ast }\left(X\right)$. We collected the independent and identically distributed dataset$D$ , we choose with parametersθ θModel of$\theta$$p_{}\left(X\right)$ , assuming data$X$ is discrete, then the purpose of log-likehood (log likelihood) is equivalent to minimizing the following publicity:
$$L\left(D\right)=\frac{1}{N}\sum _{i=1}^N(-log{p}_{}(X^{(i)}))$$

For most flow-based generative models, the process can be defined as:
$$z\sim p_{}(z)$$
$$x=g_{}(z)$$
$z$ is the latent variable,$p_{}\left(z\right)$ is a simple probability density, such as a spherical Gaussian:$p_{}(z)=N(z;0,I)$

function $g_{}$is reversible, also called bijection, giving a data $x$ , the latent variable can be passed$z=f_{}(x)=g_i^{-1}\left(x\right)$

For simplicity, below we will omit the subscript $i$

We assume the function $f$ consists of a series of transformations:$f=f_1\circ f_2\circ \cdot \cdot \cdot \circ f_n$, so $x$ sumzz$The\; relationship\; of\; z$ can be described as:

Such a sequence of reversible transformations can also be called a (regularized) flow,