Probabilistic PCA is a dimensionality reduction technique that analyzes data via a lower-dimensional latent space. The PCA probability model is a slightly modified factor analysis model that uses $\textbf{W}\textbf{W}^{T} + \sigma^{2}\textbf{I}$ as the covariance of $\textbf{x}$, where $\sigma^{2}$ is a scalar:

textbf{x} sim N(textbf{x}; textbf{b}, textbf{W}textbf{W}^{T} + sigma^{2}textbf{I})

which can be equivalently expressed as:

$\textbf{x} = \textbf{W}\textbf{h} + \textbf{b} + \sigma \textbf{z}$

where textbf{z} sim N(textbf{z}; 0, textbf{I}) is noise, $\textbf{x}$ is a data vector, $\textbf{h}$ is a latent variable, and $\textbf{W}$ is a matrix of principal axes relating the latent variables to the data.