First Learn, Then Memorize: The Spectral Bias of Diffusion Models
Diffusion models trained on a finite dataset first learn to generate novel, high-quality samples and only much later collapse onto their training set. We identify the mechanism behind this separation of timescales and the object that probes it. The training dynamics of the score function are governed---exactly, and at any width---by the Gram matrix of the Neural Tangent Kernel (NTK) evaluated on the noisy training data, so the timescales of generalization and of memorization must be encoded in its spectrum. We show that they are, and that the structure responsible has no analogue in standard kernel settings. The use of multiple noise realizations per sample ($m$ noised copies at a fixed n...
| Authors | Raphaël Urfin, Tony Bonnaire, Giulio Biroli et al. |
|---|---|
| Primary category | cs.LG |
| Published | 28 September 2026 |
| Last updated at source | 28 September 2026 |
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