Latent Abstractions in Generative Diffusion Models

Giulio Franzese, Mattia Martini, Giulio Corallo, Paolo Papotti, Pietro Michiardi

Keywords: diffusion models, world modelling, information theory, nonlinear filtering

Abstract:

In this work we study how diffusion-based generative models produce high-dimensional data, such as an image, by implicitly relying on a manifestation of a low-dimensional set of latent abstractions, that guide the generative process.
We present a novel theoretical framework that extends Nonlinear Filtering (NLF), and that offers a unique perspective on SDE-based generative models. The development of our theory relies on NLF, including a novel formulation of the joint (state and measurement) dynamics, and an information-theoretic measure of the influence of the system state on the measurement process. According to our theory, diffusion models can be cast as a system of SDE, describing a non-linear filter in which the evolution of unobservable latent abstractions steers the dynamics of an observable measurement process (corresponding to the generative pathways). In addition, we present an empirical study to validate our theory and previous empirical results on the emergence of latent abstractions at different stages of the generative process.

Primary Area: generative models

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Submission Number: 3216