Abstract
Energy-based models (EBMs) are a flexible class of deep generative models and are well-suited to capture complex dependencies in multimodal data. However, learning multimodal EBM by maximum likelihood requires Markov Chain Monte Carlo (MCMC) sampling in the joint data space, where noise-initialized Langevin dynamics often mixes poorly and fails to discover coherent inter-modal relationships. Multimodal VAEs have made progress in capturing such inter-modal dependencies by introducing a shared latent generator and a joint inference model. However, both the shared latent generator and joint inference model are parameterized as unimodal Gaussian (or Laplace), which severely limits their ability to approximate the complex structure induced by multimodal data. In this work, we study the learning problem of the multimodal EBM, shared latent generator, and joint inference model. We present a learning framework that effectively interweaves their