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.

本文研究了扩散生成模型如何通过依赖低维潜在抽象的表现来生成高维数据（如图像）。我们提出了一种新的理论框架，扩展了NLF，并为基于SDE的生成模型提供了独特视角。研究表明，扩散模型可视作SDE系统，其中不可观察的潜在抽象的演变驱动了可观察测量过程的动态。

生成扩散模型中的潜在抽象