For manifold-structured data, the authors derive explicit collapse (memorization) and optimal stopping times for empirical-score diffusion, showing the best generation occurs inside the memorization phase and the sample complexity scales with the latent dimension.
The statistical thermodynamics of generative diffusion models: Phase transitions, symmetry breaking, and critical instability
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Memorization and Generalization in Generative Diffusion under the Manifold Hypothesis
For manifold-structured data, the authors derive explicit collapse (memorization) and optimal stopping times for empirical-score diffusion, showing the best generation occurs inside the memorization phase and the sample complexity scales with the latent dimension.