Probabilistic diffusion models enjoy increasing popularity in the deep learning community. They generate convincing samples from a learned distribution of input images with a wide field of practical applications. Originally, these approaches were motivated from drift-diffusion processes, but these origins find less attention in recent, practice-oriented publications. We investigate probabilistic diffusion models from the viewpoint of scale-space research and show that they fulfil generalised scale-space properties on evolving probability distributions. Moreover, we discuss similarities and differences between interpretations of the physical core concept of drift-diffusion in the deep learning and model-based world. To this end, we examine relations of probabilistic diffusion to osmosis filters.

翻译：概率扩散模型在深度学习社区中日益受到青睐。它们从输入图像的学习分布中生成令人信服的样本，具有广泛的实际应用领域。最初，这些方法源于漂移-扩散过程，但这一起源在近期面向实践的出版物中较少受到关注。我们从尺度空间研究的角度探讨概率扩散模型，并证明它们在演化的概率分布上满足广义尺度空间性质。此外，我们讨论了深度学习领域和基于模型领域对漂移-扩散这一物理核心概念解释的异同。为此，我们研究了概率扩散与渗透滤波器之间的关系。