A Proof of Theorem

First, we prepare some lemmas. From Eq. (25), the dynamics in Eq. (26) is The results are shown in Figure 5. For VI method, we use two different models. Before each activation, we apply the layer normalization [Ba et al., 2016] to stabilize training. We run two steps of ALD iterations, i.e., We run the training iterations for 50 epochs for MNIST, SVHN, CIFAR-10 and 20 epochs for CelebA.