Multi-Component VAE with Gaussian Markov Random Field

Multi-component datasets with intricate dependencies challenge current generative modeling techniques. Existing Multi-component Variational AutoEncoders rely on simplified aggregation strategies that compromise structural coherence across generated components. We introduce the Gaussian Markov Random Field Multi-Component Variational AutoEncoder, embedding Gaussian Markov Random Fields into both prior and posterior distributions to explicitly model cross-component relationships. This enables richer representation and faithful reproduction of complex interactions. Empirically, our model achieves state-of-the-art performance on a synthetic Copula dataset designed for intricate component relationships, competitive results on PolyMNIST, and significantly enhanced structural coherence on the real-world BIKED dataset, demonstrating its suitability for applications demanding robust multi-component coherence.