1 citations · 3 across the 6 of their papers we have counts for
6 papers
Emergence of Distortions in High-Dimensional Guided Diffusion Models
Enrico Ventura, Beatrice Achilli, Luca Ambrogioni +1
Classifier-free guidance (CFG) is the de facto standard for conditional sampling in diffusion models, yet it often reduces sample diversity. Using tools from statistical physics, w…
The Capacity of Modern Hopfield Networks under the Data Manifold Hypothesis
Beatrice Achilli, Luca Ambrogioni, Carlo Lucibello +2
We generalize the computation of the capacity of exponential Hopfield model from Lucibello and Mézard (2024) to more generic pattern ensembles, including binary patterns and patter…
Memorization and Generalization in Generative Diffusion under the Manifold Hypothesis
Beatrice Achilli, Luca Ambrogioni, Carlo Lucibello +2
We study the memorization and generalization capabilities of Diffusion Models (DMs) when data lies on a structured latent manifold. Specifically, we consider a set of data poin…
Losing dimensions: Geometric memorization in generative diffusion
Beatrice Achilli, Enrico Ventura, Gianluigi Silvestri +5
Diffusion models power leading generative AI, but when and how they memorize training data, especially on low-dimensional manifolds, remains unclear. We find memorization emerges g…
Manifolds, Random Matrices and Spectral Gaps: The geometric phases of generative diffusion
Enrico Ventura, Beatrice Achilli, Gianluigi Silvestri +2
In this paper, we investigate the latent geometry of generative diffusion models under the manifold hypothesis. For this purpose, we analyze the spectrum of eigenvalues (and singul…
Finite Size Corrections to Disordered Systems : mean field results and applications to finite dimensional models
Carlo Lucibello
This PhD thesis has the following structure: Chapter 1 - General introduction; Chapter 2 - Preliminaries; Chapter 3 - The Replicated Transfer Matrix; Chapter 4 - Finite Size Correc…