arXiv:2602.04780cs.LGcond-mat.dis-nn2026-02被引 4

揭示多模态扩散模型生成中的动态相变机制,解释为何不同模式会不同步。

Dynamical Regimes of Multimodal Diffusion Models

  • 用耦合奥恩斯坦-乌伦贝克过程建模多模态扩散,分析时间尺度谱
  • 发现生成中存在同步间隙,导致不同模式稳定时间不同
  • 提出可调耦合强度作为时间滤波器,适合优化生成调度

基于扩散的生成模型在高维数据合成上取得了前所未有的保真度,但多模态生成的理论机制仍不清晰。本文提出一个耦合扩散模型的理论框架,采用耦合奥恩斯坦-乌伦贝克过程作为可解析模型。通过非平衡统计物理中的动力学相变理论,证明多模态生成由相互作用的时间尺度谱决定,而非同时收敛。关键发现是“同步间隙”——反向生成过程中,不同本征模态以不同速率稳定,为常见的不同步伪影提供理论解释。我们推导了对称与非各向同性耦合下物种分化与崩溃的时间条件,建立了避免不稳定对称性破缺的耦合强度严格边界。结果表明,耦合强度充当谱滤波器,可调控生成的时间层次结构。通过在MNIST数据集上训练的扩散模型和精确得分采样器进行受控实验验证。这些发现支持针对特定模式时间尺度设计时变耦合策略,可能替代经验性的指导调节。

原文摘要 · Abstract (English)

Diffusion based generative models have achieved unprecedented fidelity in synthesizing high dimensional data, yet the theoretical mechanisms governing multimodal generation remain poorly understood. Here, we present a theoretical framework for coupled diffusion models, using coupled Ornstein-Uhlenbeck processes as a tractable model. By using the nonequilibrium statistical physics of dynamical phase transitions, we demonstrate that multimodal generation is governed by a spectral hierarchy of interaction timescales rather than simultaneous resolution. A key prediction is the ``synchronization gap'', a temporal window during the reverse generative process where distinct eigenmodes stabilize at different rates, providing a theoretical explanation for common desynchronization artifacts. We derive analytical conditions for speciation and collapse times under both symmetric and anisotropic coupling regimes, establishing strict bounds for coupling strength to avoid unstable symmetry breaking. We show that the coupling strength acts as a spectral filter that enforces a tunable temporal hierarchy on generation. We support these predictions through controlled experiments with diffusion models trained on MNIST datasets and exact score samplers. These results motivate time dependent coupling schedules that target mode specific timescales, offering a potential alternative to ad hoc guidance tuning.

扩散模型多模态动态系统

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