Diagonal Gaussian Variational Approximation
Definition
A diagonal Gaussian variational approximation is a multivariate Gaussian whose covariance matrix is diagonal:
$$q_\phi(z)=\mathcal N(z\mid \mu,\mathrm{diag}(\sigma_1^2,\dots,\sigma_D^2)).$$Why it matters in Q1
It is a concrete parametric mean-field family. Each latent dimension has its own mean and variance, but no covariance terms are allowed.