variational approximation introduces a distribution Q over the latent variable Z and to the extent that this distribution Q is closer to the true posterior over the latent variables we're able to make it bound that becomes tighter and tighter and does a better job of lower bounding the true density unfortunately this model is only asymptotically consistent if this Q distribution is perfect otherwise there's a gap between the lower bound and the actual density so even if the optimizer is perfect and even if we have infinite training data