Variational Bayes (VB) replaces exact Bayesian inference with an optimization problem: find a tractable distribution q(z) that minimizes KL(q || p), the Kullback-Leibler divergence from q to the true posterior p(z|x). This is equivalent to maximizing the Evidence Lower BOund (ELBO): log p(x) ≥ E_q[log p(x,z)] − E_q[log q(z)]. The mean-field approximation assumes q factorizes across latent variables, yielding coordinate-ascent update equations. VB is faster than MCMC and scales to large datasets, but tends to underestimate posterior variance — the zero-forcing behavior of forward KL vs reverse KL. The orange distribution approximates the blue true posterior; watch the ELBO climb as the variational parameters adapt.