Abstract

How do generative AI systems, such as diffusion models, learn to create new data? I will argue that natural data – such as images or text – can be described as hierarchical compositions of features, which generative models learn to recombine in novel ways. To analyze this mechanism, I will introduce ensembles of synthetic grammars as models of structured data. Within this framework, I will present a theory of composition that predicts a phase transition in the generative dynamics of diffusion models, confirmed in modern architectures trained on real-world datasets. In the second part of the talk, I will discuss how such grammars can be learned: what statistical correlations a learner can exploit to infer grammatical structure and the sample complexity required to do so. This analysis shows that diffusion models progressively build internal representations corresponding to increasingly abstract latent variables, a procedure reminiscent of the renormalization group in physics.