扩散模型生成图案的机制,本质是噪声中出现的非平衡相变。
How Out-of-Equilibrium Phase Transitions can Seed Pattern Formation in Trained Diffusion Models
- 将去噪过程视为非平衡相变,低频模式失稳触发结构形成。
- 在关键时间点,相关长度突增,低频模式软化,理论预测精准。
- 该阶段干预能显著提升类别对齐,适合优化生成质量。
扩散模型通过逐步将噪声转化为数据生成结构,但其内在机制仍不清晰。本文揭示,训练后扩散模型中的模式形成可解释为由去噪动力学不稳定性引发的非平衡相变。我们构建了理论框架,将数据对称性与架构约束(如局部性和平移等变性)关联至集体空间模式的涌现。当低频模式失稳时,空间相关性迅速增长,使噪声组织成有序图案。通过分析模型与实验验证:在受控的分块模型中,相关长度在临界时刻急剧上升,低频模式同步软化,与理论预测一致;在Fashion-MNIST和ImageNet的卷积扩散模型中,同样观测到相关长度峰值与空间模式减弱;干预实验表明,在此临界阶段施加引导,比随机时机显著提升类别对齐效果,证明该阶段兼具描述性与功能性重要性。
原文摘要 · Abstract (English)
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 validate this theory through a combination of analytical models and experiments. In a controlled patch-based model, we observe a sharp increase in correlation length and a simultaneous softening of low-frequency modes at a well-defined critical time, accurately predicted by theory. Similar signatures are found in trained convolutional diffusion models on Fashion-MNIST and in large-scale ImageNet models, where pattern formation coincides with a peak in estimated correlation length and a pronounced weakening of spatial modes. Finally, intervention experiments show that applying guidance precisely at this critical stage significantly improves class alignment compared to applying it at random times, demonstrating that this regime is not only descriptive but functionally important.
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