用熵变化追踪扩散模型生成中的语义分化时机
The Entropic Signature of Class Speciation in Diffusion Models
- 通过追踪噪声状态下的类别条件熵，识别语义分化的关键时间窗口
- 在高维混合高斯模型和EDM2-XS、Stable Diffusion中验证了熵的集中性
- 适合研究扩散模型动态机制或做时序控制的研究者
扩散模型并非均匀地恢复语义结构，而是样本在狭窄的时间范围内从语义模糊转向类别确定。已有理论将这一转变归因于类别分离方向上的动力学不稳定性，但实际检测与利用训练后模型中的此类窗口仍受限。本文表明，跟踪给定噪声状态下的潜在语义变量的类别条件熵，可可靠识别这些过渡阶段。通过限制熵到语义划分，该方法还能解析不同抽象层次的语义决策。我们在高维高斯混合模型中分析此行为，发现熵速率集中在与之前发现的保持方差扩散中物种对称性破缺相同的对数时间尺度上。在EDM2-XS和Stable Diffusion 1.5上的验证显示，类别条件熵始终能定位形成语义结构的关键噪声区间。最后，我们利用该框架量化了引导如何随时间重分布语义信息。这些结果连接了信息论与统计物理视角下的扩散过程，为时间局部控制提供了原则性基础。
原文摘要 · Abstract (English)
Diffusion models do not recover semantic structure uniformly over time. Instead, samples transition from semantic ambiguity to class commitment within a narrow regime. Recent theoretical work attributes this transition to dynamical instabilities along class-separating directions, but practical methods to detect and exploit these windows in trained models are still limited. We show that tracking the class-conditional entropy of a latent semantic variable given the noisy state provides a reliable signature of these transition regimes. By restricting the entropy to semantic partitions, the entropy can furthermore resolve semantic decisions at different levels of abstraction. We analyze this behavior in high-dimensional Gaussian mixture models and show that the entropy rate concentrates on the same logarithmic time scale as the speciation symmetry-breaking instability previously identified in variance-preserving diffusion. We validate our method on EDM2-XS and Stable Diffusion 1.5, where class-conditional entropy consistently isolates the noise regimes critical for semantic structure formation. Finally, we use our framework to quantify how guidance redistributes semantic information over time. Together, these results connect information-theoretic and statistical physics perspectives on diffusion and provide a principled basis for time-localized control.
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