# Multi-Component VAE with Gaussian Markov Random Field

arXiv: https://arxiv.org/abs/2507.12165 · HTML: https://mlsanity.com/paper/2507.12165/

## Key facts

- Cited by 2 papers in the map (data through 14 Oct 2026).
- Builds on 20 of its 59 references that are in the map.
- First posted on arXiv 16 Jul 2025.

## Builds on (most cited first, 20 of 20)

- [Classifier-Free Diffusion Guidance](https://mlsanity.com/paper/2207.12598/) (2022)
- [An Introduction to Variational Autoencoders](https://mlsanity.com/paper/1906.02691/) (2019)
- [NVAE: A Deep Hierarchical Variational Autoencoder](https://mlsanity.com/paper/2007.03898/) (2020)
- [MM-Diffusion: Learning Multi-Modal Diffusion Models for Joint Audio and Video Generation](https://mlsanity.com/paper/2212.09478/) (2022)
- [Multimodal Generative Models for Scalable Weakly-Supervised Learning](https://mlsanity.com/paper/1802.05335/) (2018)
- [Variational Mixture-of-Experts Autoencoders for Multi-Modal Deep Generative Models](https://mlsanity.com/paper/1911.03393/) (2019)
- [Composing graphical models with neural networks for structured representations and fast inference](https://mlsanity.com/paper/1603.06277/) (2016)
- [Seeing and Hearing: Open-domain Visual-Audio Generation with Diffusion Latent Aligners](https://mlsanity.com/paper/2402.17723/) (2024)
- [Joint Multimodal Learning with Deep Generative Models](https://mlsanity.com/paper/1611.01891/) (2016)
- [Generalized Multimodal ELBO](https://mlsanity.com/paper/2105.02470/) (2021)
- [Multimodal Generative Learning Utilizing Jensen-Shannon-Divergence](https://mlsanity.com/paper/2006.08242/) (2020)
- [Generative Models of Visually Grounded Imagination](https://mlsanity.com/paper/1705.10762/) (2017)
- [BIKED: A Dataset for Computational Bicycle Design with Machine Learning Benchmarks](https://mlsanity.com/paper/2103.05844/) (2021)
- [MMDisCo: Multi-Modal Discriminator-Guided Cooperative Diffusion for Joint Audio and Video Generation](https://mlsanity.com/paper/2405.17842/) (2024)
- [Efficient Learning of Discrete Graphical Models](https://mlsanity.com/paper/1902.00600/) (2019)
- [Statistical Guarantees for Variational Autoencoders using PAC-Bayesian Theory](https://mlsanity.com/paper/2310.04935/) (2023)
- [Multimodal Deep Learning for Finance: Integrating and Forecasting International Stock Markets](https://mlsanity.com/paper/1903.06478/) (2019)
- [AircraftVerse: A Large-Scale Multimodal Dataset of Aerial Vehicle Designs](https://mlsanity.com/paper/2306.05562/) (2023)
- [GumBolt: Extending Gumbel trick to Boltzmann priors](https://mlsanity.com/paper/1805.07349/) (2018)
- [Learning Graphical Models With Hubs](https://mlsanity.com/paper/1402.7349/) (2014)

## Built on by (most cited first, 2 of 2)

- [H"older++: Improving the Quality-Coherence Trade-off in Multimodal VAEs](https://mlsanity.com/paper/2606.13381/) (2026)
- [Generative Bayesian Filtering for State Estimation](https://mlsanity.com/paper/2607.20521/) (2026)

## Abstract (arXiv)

Multi-component datasets with intricate dependencies, like industrial assemblies or multi-modal imaging, challenge current generative modeling techniques. Existing Multi-component Variational AutoEncoders typically rely on simplified aggregation strategies, neglecting critical nuances and consequently compromising structural coherence across generated components. To explicitly address this gap, we introduce the Gaussian Markov Random Field Multi-Component Variational AutoEncoder , a novel generative framework embedding Gaussian Markov Random Fields into both prior and posterior distributions. This design choice explicitly models cross-component relationships, enabling richer representation and faithful reproduction of complex interactions. Empirically, our GMRF MCVAE achieves state-of-the-art performance on a synthetic Copula dataset specifically constructed to evaluate intricate component relationships, demonstrates competitive results on the PolyMNIST benchmark, and significantly enhances structural coherence on the real-world BIKED dataset. Our results indicate that the GMRF MCVAE is especially suited for practical applications demanding robust and realistic modeling of multi-component coherence