Generative AI models that create images, audio, or other data often work by starting from random noise and gradually removing it in many small steps, following a learned direction. This process is called deterministic diffusion sampling. Until now, it was unclear whether the path the data takes during this removal follows any general rule.
The authors examined sampling trajectories from many different trained on very different kinds of data, including images and other modalities. They found that all these trajectories share the same basic curved shape, a hyperbolic geometry. They showed that this shape can be explained by a simple mathematical model that uses the best possible linear way to remove noise at each step.
This finding means that despite the huge complexity of modern AI models, their internal sampling behavior follows a simple, predictable pattern. This universality could lead to new ways to speed up training or find the best settings for generating data, making these powerful tools more efficient and easier to understand.