Real diffusion models trained on MNIST, CIFAR-10, and CelebA show score-Jacobian spectral gaps matching random-matrix-theory predictions for sub-manifold dimensionality
measured in 1 paperA statistical-physics/random-matrix treatment of the score-matching objective predicts that the eigenvalue spectrum of a diffusion model's score-function Jacobian develops sharp gaps as sampling noise decreases, with gap locations revealing the dimensionality of underlying data sub-manifolds [ventura-etal-2025-geometric-phases-generative-diffusion] Real diffusion models trained from scratch on real MNIST, CIFAR-10, and CelebA image datasets have their score-Jacobian eigenspectra numerically computed along the denoising trajectory, confirming the predicted spectral gaps emerge as noise decreases, with gap locations tracking each dataset's estimated intrinsic sub-manifold dimensionality [ventura-etal-2025-geometric-phases-generative-diffusion] The emergence of each spectral gap marks a distinct geometric phase transition in the generative dynamics, empirically validating the closed-form phase-diagram predictions derived under the paper's statistical-physics framework on real, natural (non-toy) image data [ventura-etal-2025-geometric-phases-generative-diffusion]