Diffusion probabilistic models excel at sampling new images from learned distributions. Originally motivated by drift-diffusion concepts from physics, they apply image perturbations such as noise and blur in a forward process that results in a tractable probability distribution. A corresponding learned reverse process generates images and can be conditioned on side information, which leads to a wide variety of practical applications. Most of the research focus currently lies on practice-oriented extensions. In contrast, the theoretical background remains largely unexplored, in particular the relations to drift-diffusion. In order to shed light on these connections to classical image filtering, we propose a generalised scale-space theory for diffusion probabilistic models. Moreover, we show conceptual and empirical connections to diffusion and osmosis filters.

翻译：扩散概率模型在从学习到的分布中采样新图像方面表现出色。最初受物理学中的漂移-扩散概念启发，这类模型在前向过程中施加噪声和模糊等图像扰动，从而得到易于处理的概率分布。对应的学习反向过程可生成图像，并能以辅助信息为条件，这带来了多样化的实际应用。目前大多数研究聚焦于实践导向的扩展，而理论背景——尤其是与漂移-扩散的关联——在很大程度上尚未被探索。为阐明这类模型与经典图像滤波的联系，我们提出了扩散概率模型的广义尺度空间理论。此外，我们展示了其与扩散及渗透滤波器的概念关联和实证联系。