Geometric regularity in deterministic sampling dynamics of diffusion-based generative models

What is it about?

In this paper, we discover the fundamental laws that govern the sampling dynamics of diffusion-based generative models. We show that each deterministic sampling trajectory along the model’s gradient field lies within an extremely low-dimensional subspace, and, remarkably, all trajectories share an almost identical “boomerang” geometry—regardless of model architecture, applied conditions, or generated content. We characterize the mathematical properties of these trajectories and develop a state-of-the-art fast-sampling algorithm.

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Photo by Marek Piwnicki on Unsplash

Photo by Marek Piwnicki on Unsplash