A Proof of Theorem

First, we prepare some lemmas. From Eq. (25), the dynamics in Eq. (26) is equivalent to Eq. (22) and Eq. In the following, we prove Theorem 1 using the above lemmas. B.1 Neural likelihood example We perform an experiment with a complex posterior, wherein the likelihood is defined with a randomly initialized neural network f The results are shown in Figure 5. The left three columns show the density visualizations of the ground truth or approximation posteriors of VI methods; the right two columns show the visualizations of 2D histograms and samples obtained using ALD.