Ventura et al. (2025) Custom Score-Based Diffusion Models — Math in LLMs Research Map

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Ventura et al. (2025) Custom Score-Based Diffusion Models

Research (Ventura, Achilli, Silvestri, Lucibello & Ambrogioni; custom-trained from scratch, arXiv:2410.05898)

Structures found in this family (1)

Curvature profile of the representation manifold

By model (3)

Score-based diffusion model (custom-trained, CelebA)

Curvature profile of the representation manifold

Score-based diffusion model (custom-trained, CIFAR-10)

Curvature profile of the representation manifold

Score-based diffusion model (custom-trained, MNIST)

Curvature profile of the representation manifold

Observations (1)

Real diffusion models trained on MNIST, CIFAR-10, and CelebA show score-Jacobian spectral gaps matching random-matrix-theory predictions for sub-manifold dimensionality

Papers

Manifolds, Random Matrices and Spectral Gaps: The Geometric Phases of Generative Diffusion (2025)