Learning Adaptive Multi-Stage Energy-based Prior for Hierarchical Generative Model

Hierarchical generative models represent data with multiple layers of latent variables organized in a top-down structure. These models typically assume Gaussian priors for multi-layer latent variables, which lack expressivity for the contextual dependencies among latents, resulting in a distribution gap between the prior and the learned posterior. Recent works have explored hierarchical energy-based prior models (EBMs) as a more expressive alternative to bridge this gap. However, most approaches learn only a single EBM, which can be ineffective when the target distribution is highly multi-modal and multi-scale across hierarchical layers of latent variables. In this work, we propose a framework that learns multi-stage hierarchical EBM priors, where a sequence of adaptive stages progressively refines the prior to match the posterior. Our method supports both joint training with the generator and a more efficient two-phase strategy for deeper hierarchies. Experiments across standard benchmarks show that our approach consistently generates higher-quality images and learns richer hierarchical representations.