发表机构
The Hong Kong University of Science and Technology（香港科技大学）
机构由 AI 辅助整理，请以论文原文为准。AI 中文总结
本研究针对扩散模型采样流程修改引入的扰动问题，构建结合动力学分析与信息论的理论框架，量化扰动强度并推导响应恒等式，经实验验证可诊断缓存加速带来的采样误差。
AI 中文摘要
扩散模型在生成建模领域取得了显著成功，其采样流程常被修改以控制生成过程并提升效率。这些修改会在采样轨迹中引入扰动，由此产生一个核心问题：此类扰动如何影响生成的输出？为解决该问题，我们开发了一套理论框架来研究扰动传播，将采样过程的动力学分析与输出响应的信息论表征相结合。在该框架内，我们用受扰动轨迹分布与参考轨迹分布之间的Kullback-Leibler（KL）散度（称为路径代价）来量化扰动强度，研究表明路径代价可对输出分布的变化进行约束，但无法决定这些变化。基于此分析，我们推导了一个响应恒等式，该恒等式将局部扰动的传播与累积和选定特征均值所捕获的信息关联起来，解释了为何输出分布的变化可能无法被其一阶响应检测到。我们通过在预训练扩散模型中以相等路径成本进行受控干预来验证该理论分析，揭示了采样阶段和空间频率上不同的输出敏感性模式。为评估我们的框架是否能诊断实际近似产生的扰动，我们将其应用于基于缓存的加速，结果表明我们的传播分析可可靠识别出缓存导致图像误差更大的采样区间。
英文摘要
Diffusion models have achieved remarkable success in generative modeling, with their sampling procedures routinely modified to control generation and improve efficiency. These modifications introduce perturbations along the sampling trajectory, raising a central question: how do such perturbations affect generated output? To address this question, we develop a theoretical framework to investigate perturbation propagation, combining dynamical analysis of the sampling process with an information-theoretic characterization of output responses. Within this framework, we quantify perturbation strength using the Kullback--Leibler (KL) divergence between perturbed and reference trajectory distributions, termed as path cost, which is shown to bound, but do not determine, changes in the output distribution. Building on this analysis, we derive a response identity that connects the propagation and accumulation of local perturbations with the information captured by a selected feature mean, explaining why changes in the output distribution can remain undetected by its first-order response. We test our theoretical analysis through controlled interventions at equal path cost in pretrained diffusion models, revealing distinct patterns of output sensitivity across sampling stages and spatial frequencies. To assess whether our framework can diagnose perturbations arising from practical approximations, we apply it to cache-based acceleration and show that our propagation analysis reliably identifies sampling intervals where caching causes larger image errors.
