12 papers
WaiT for the Signal: Simple Frequency-Aware Flow-Matching
Krunoslav Lehman Pavasovic, Théophane Vallaeys, Stéphane Mallat +4
As image generation models scale to ever higher resolutions, global coherence, local detail, and texture fidelity become critical axes for generation quality. However, standard flo…
The critical slowing down in diffusion models
Luca Maria Del Bono, Giulio Biroli, Patrick Charbonneau +1
Computational sampling has been central to the sciences since the mid-20th century. While machine-learning-based approaches have recently enabled major advances, their behavior rem…
Discontinuous BBP transitions
Dario Bocchi, Giulio Biroli, Chiara Cammarota +1
The Baik-Ben Arous-Peche (BBP) transition sets fundamental limits for detecting low-rank structure in noisy high-dimensional data and underlies a wide range of spectral methods in…
Theory of Speciation Transitions in Diffusion Models with General Class Structure
Beatrice Achilli, Marco Benedetti, Giulio Biroli +1
Diffusion Models generate data by reversing a stochastic diffusion process, progressively transforming noise into structured samples drawn from a target distribution. Recent theore…
Eigenvalue spectral tails and localization properties of asymmetric networks
Pietro Valigi, Joseph W. Baron, Izaak Neri +2
In contrast to the neatly bounded spectra of densely populated large random matrices, sparse random matrices often exhibit unbounded eigenvalue tails on the real and imaginary axis…
Why Diffusion Models Don't Memorize: The Role of Implicit Dynamical Regularization in Training
Tony Bonnaire, Raphaël Urfin, Giulio Biroli +1
Diffusion models have achieved remarkable success across a wide range of generative tasks. A key challenge is understanding the mechanisms that prevent their memorization of traini…