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Probabilistic Circuits (PCs) are a unified framework for tractableprobabilistic models that support efficient computation of variousprobabilistic queries (e.g., marginal probabilities). One key challenge is toscale PCs to model large and high-dimensional real-world datasets: we observethat as the number of parameters in PCs increases, their performanceimmediately plateaus. This phenomenon suggests that the existing optimizersfail to exploit the full expressive power of large PCs. We propose to overcomesuch bottleneck by latent variable distillation: we leverage the less tractablebut more expressive deep generative models to provide extra supervision overthe latent variables of PCs. Specifically, we extract information fromTransformer-based generative models to assign values to latent variables ofPCs, providing guidance to PC optimizers. Experiments on both image andlanguage modeling benchmarks (e.g., ImageNet and WikiText-2) show that latentvariable distillation substantially boosts the performance of large PCscompared to their counterparts without latent variable distillation. Inparticular, on the image modeling benchmarks, PCs achieve competitiveperformance against some of the widely-used deep generative models, includingvariational autoencoders and flow-based models, opening up new avenues fortractable generative modeling.

Scaling Up Probabilistic Circuits by Latent Variable Distillation