Diffusion-based generative modeling has emerged as a general computational framework for simulating high-dimensional, structured data across various domains.
Understanding its generative mechanisms is paramount for advancing model training and inference in a principled way.
Here, we demonstrate that deterministic sampling trajectories share a universal geometric structure invariant to data modalities and diffusion model implementations.
This structure can be largely explained by an exactly solvable model based on the optimal linear denoiser.