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

翻译：具有复杂依赖关系的多组件数据集（如工业装配体或多模态成像）对当前生成建模技术提出挑战。现有多组件变分自编码器通常采用简化的聚合策略，忽视了关键细节，从而损害了生成组件之间的结构一致性。为明确解决这一问题，我们提出高斯马尔可夫随机场多组件变分自编码器（GMRF MCVAE），这是一种将高斯马尔可夫随机场引入先验分布与后验分布的新型生成框架。该设计选择显式建模跨组件关系，能够更丰富地表示并忠实再现复杂交互。实验结果表明，我们的GMRF MCVAE在专门为评估复杂组件关系而构建的合成Copula数据集上达到了最先进性能，在PolyMNIST基准测试中展现了具有竞争力的结果，并在真实世界的BIKED数据集上显著增强了结构一致性。研究结果表明，GMRF MCVAE尤其适用于需要对多组件一致性进行稳健且逼真建模的实际应用场景。