揭示扩散模型生成图像时依赖低维潜在抽象的内在机制
Latent Abstractions in Generative Diffusion Models
- 将扩散模型视为非线性滤波系统，潜变量驱动可观测生成路径
- 理论证明潜变量在生成过程中持续影响测量过程的演化
- 适合研究生成模型机理与潜在表征的学者参考
本文研究基于扩散的生成模型如何通过隐含的低维潜变量抽象生成高维数据（如图像）。我们提出一个扩展的NLF理论框架，从随机微分方程（SDE）视角理解生成过程。该理论建立在联合状态与观测动态的新表述之上，并引入信息论度量来刻画系统状态对观测过程的影响。根据此理论，扩散模型可被看作一个非线性滤波系统：不可观测的潜变量抽象引导可观测测量过程的演化（即生成路径）。此外，我们通过实证研究验证了该理论，并确认了潜变量在生成不同阶段的涌现现象。
原文摘要 · Abstract (English)
In this work we study how diffusion-based generative models produce high-dimensional data, such as an image, by implicitly relying on a manifestation of a low-dimensional set of latent abstractions, that guide the generative process. We present a novel theoretical framework that extends NLF, and that offers a unique perspective on SDE-based generative models. The development of our theory relies on a novel formulation of the joint (state and measurement) dynamics, and an information-theoretic measure of the influence of the system state on the measurement process. According to our theory, diffusion models can be cast as a system of SDE, describing a non-linear filter in which the evolution of unobservable latent abstractions steers the dynamics of an observable measurement process (corresponding to the generative pathways). In addition, we present an empirical study to validate our theory and previous empirical results on the emergence of latent abstractions at different stages of the generative process.
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