Score-Based Diffusion meets Annealed Importance Sampling

More than twenty years after its introduction, Annealed Importance Sampling (AIS) remains one of the most effective methods for marginal likelihood estimation. It relies on a sequence of distributions interpolating between a tractable initial distribution and the target distribution of interest which we simulate from approximately using a non-homogeneous Markov chain. To obtain an importance sampling estimate of the marginal likelihood, AIS introduces an extended target distribution to reweight the Markov chain proposal. While much effort has been devoted to improving the proposal distribution used by AIS, by changing the intermediate distributions and corresponding Markov kernels, an underappreciated issue is that AIS uses a convenient but suboptimal extended target distribution. This can hinder its performance.