Hierarchical Semi-Implicit Variational Inference with Application to Diffusion Model Acceleration
This work addresses a bottleneck in variational inference for researchers in machine learning, offering an incremental improvement over existing SIVI methods.
The paper tackles the limited expressiveness of single-layer semi-implicit variational inference (SIVI) for complex posterior distributions by proposing hierarchical SIVI (HSIVI), a multi-layer extension that improves performance on Bayesian inference tasks and accelerates diffusion model sampling, achieving high-quality samples with fewer function evaluations.
Semi-implicit variational inference (SIVI) has been introduced to expand the analytical variational families by defining expressive semi-implicit distributions in a hierarchical manner. However, the single-layer architecture commonly used in current SIVI methods can be insufficient when the target posterior has complicated structures. In this paper, we propose hierarchical semi-implicit variational inference, called HSIVI, which generalizes SIVI to allow more expressive multi-layer construction of semi-implicit distributions. By introducing auxiliary distributions that interpolate between a simple base distribution and the target distribution, the conditional layers can be trained by progressively matching these auxiliary distributions one layer after another. Moreover, given pre-trained score networks, HSIVI can be used to accelerate the sampling process of diffusion models with the score matching objective. We show that HSIVI significantly enhances the expressiveness of SIVI on several Bayesian inference problems with complicated target distributions. When used for diffusion model acceleration, we show that HSIVI can produce high quality samples comparable to or better than the existing fast diffusion model based samplers with a small number of function evaluations on various datasets.