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Semi-implicit variational inference (SIVI) has been introduced to expand theanalytical variational families by defining expressive semi-implicitdistributions in a hierarchical manner. However, the single-layer architecturecommonly used in current SIVI methods can be insufficient when the targetposterior has complicated structures. In this paper, we propose hierarchicalsemi-implicit variational inference, called HSIVI, which generalizes SIVI toallow more expressive multi-layer construction of semi-implicit distributions.By introducing auxiliary distributions that interpolate between a simple basedistribution and the target distribution, the conditional layers can be trainedby progressively matching these auxiliary distributions one layer afteranother. Moreover, given pre-trained score networks, HSIVI can be used toaccelerate the sampling process of diffusion models with the score matchingobjective. We show that HSIVI significantly enhances the expressiveness of SIVIon several Bayesian inference problems with complicated target distributions.When used for diffusion model acceleration, we show that HSIVI can produce highquality samples comparable to or better than the existing fast diffusion modelbased samplers with a small number of function evaluations on various datasets.

Hierarchical Semi-Implicit Variational Inference with Application to Diffusion Model Acceleration