  The field of image generation has made significant progress thanks to the
introduction of Diffusion Models, which learn to progressively reverse a given
image corruption. Recently, a few studies introduced alternative ways of
corrupting images in Diffusion Models, with an emphasis on blurring. However,
these studies are purely empirical and it remains unclear what is the optimal
procedure for corrupting an image. In this work, we hypothesize that the
optimal procedure minimizes the length of the path taken when corrupting an
image towards a given final state. We propose the Fisher metric for the path
length, measured in the space of probability distributions. We compute the
shortest path according to this metric, and we show that it corresponds to a
combination of image sharpening, rather than blurring, and noise deblurring.
While the corruption was chosen arbitrarily in previous work, our Shortest Path
Diffusion (SPD) determines uniquely the entire spatiotemporal structure of the
corruption. We show that SPD improves on strong baselines without any
hyperparameter tuning, and outperforms all previous Diffusion Models based on
image blurring. Furthermore, any small deviation from the shortest path leads
to worse performance, suggesting that SPD provides the optimal procedure to
corrupt images. Our work sheds new light on observations made in recent works
and provides a new approach to improve diffusion models on images and other
types of data.
