The critical slowing down in training diffusion models
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 remains poorly understood, with limited theoretical control over when and why they succeed. Here we provide such insight for diffusion models---a class of generative schemes highly effective in practice---by analyzing their application to the $O(n)$ model of statistical field theory in the Gaussian limit $n \to \infty$. In this analytically tractable setting, we show that training a score model with a one-layer network architecture matching the exact solution exhibits a form of critical slowing down in parameter le...
| Authors | Luca Maria Del Bono, Giulio Biroli, Patrick Charbonneau et al. |
|---|---|
| Primary category | cond-mat.dis-nn |
| Published | 12 May 2026 |
| Last updated at source | 18 September 2026 |
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