Latent Abstractions in Generative Diffusion Models

In this work, we study how diffusion-based generative models produce high-dimensional data, such as images, by relying on latent abstractions that guide the generative process. We introduce a novel theoretical framework extending Nonlinear Filtering (NLF), offering a new perspective on SDE-based generative models. Our theory is based on a new formulation of joint (state and measurement) dynamics and an information-theoretic measure of state influence on the measurement process. We show that diffusion models can be interpreted as a system of SDE, describing a non-linear filter where unobservable latent abstractions steer the dynamics of an observable measurement process. Additionally, we present an empirical study validating our theory and supporting previous findings on the emergence of latent abstractions at different generative stages.