  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.
