How Out-of-Equilibrium Phase Transitions can Seed Pattern Formation in Trained Diffusion Models
Diffusion models generate structure by progressively transforming noise into data, yet the mechanisms underlying this transition remain poorly understood. In this work, we show that pattern formation in trained diffusion models can be explained as an out-of-equilibrium phase transition driven by instabilities in the denoising dynamics. We develop a theoretical framework linking data symmetries and architectural constraints, such as locality and translation equivariance, to the emergence of collective spatial modes. In this view, structure arises when low-frequency modes become unstable, triggering a rapid growth of spatial correlations that organizes noise into coherent patterns. We valid...
| Authors | Luca Ambrogioni |
|---|---|
| Primary category | cs.LG |
| Published | 20 March 2026 |
| Last updated at source | 13 October 2026 |
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