The most common type of variational Bayes, known as mean-field variational Bayes, uses the Kullback-Leibler divergence (KL-divergence) of P from Q as the choice of dissimilarity function.
D_{\mathrm{KL}}(Q || P) = \sum_\mathbf{Z} Q(\mathbf{Z}) \log \frac{Q(\mathbf{Z})}{P(\mathbf{Z}\mid \mathbf{X})}.