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 gen...

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Bibliographic Details
Published in:Entropy (Basel, Switzerland) Vol. 27; no. 4; p. 371
Main Authors: Franzese, Giulio, Martini, Mattia, Corallo, Giulio, Papotti, Paolo, Michiardi, Pietro
Format: Journal Article
Language:English
Published: Switzerland MDPI AG 31.03.2025
MDPI
Subjects:
Analysis
Brownian motion
Computational linguistics
Diffusion models
Information theory
Language processing
Natural language interfaces
nonlinear filtering
Random variables
world modeling
Germany
Michigan
information theory
nonlinear filtering
diffusion models
world modeling
ISSN:1099-4300, 1099-4300
Online Access:Get full text
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Summary: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.
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ISSN:1099-4300
1099-4300
DOI:10.3390/e27040371