🤖 AI Summary
This study quantifies the amplification effect of early perturbations on subsequent steps in diffusion model sampling. For the first time, this work directly compares “shaped” noise derived from historical trajectories with newly sampled “fresh” noise, systematically revealing their differential impacts on generative updates through paired angular gain analysis, latent-space RMS measurements, and perceptual feature evaluations. The results demonstrate that shaped noise yields angular gain ratios ranging from 1.14 to 2.35, with such gains being highly dependent on trajectory alignment. By elucidating how structured noise propagates differently than uncorrelated noise throughout the denoising process, this research provides a novel perspective for understanding error propagation mechanisms in diffusion sampling. Furthermore, it establishes a theoretical foundation for optimizing sampling strategies in generative modeling.
📝 Abstract
How strongly do the remaining diffusion-sampling steps amplify a perturbation at a late latent state? Standard measurements answer this question with newly sampled isotropic noise, even though perturbations encountered during sampling have already been transformed by earlier steps. We compare these two cases directly. For each trajectory, we transport a centered perturbation from an earlier step to a late state, then replay its direction at the same magnitude as a newly sampled isotropic perturbation; both then undergo the same remaining updates. Across the samplers we study, median paired shaped-to-fresh angular-gain ratios range from $1.14$ to $2.35$. Shaped angular gain exceeds its matched fresh counterpart in every trajectory in the original main cohorts. The same pattern appears when endpoint change is measured by latent RMS. The effect also appears in perceptual feature representations: earlier-sampling directions cause larger feature changes at the endpoint, even when the corresponding pixel-space change is comparable. Permuting shaped directions across trajectories weakens the effect, including within class, indicating that the advantage depends on alignment with the receiving trajectory as well as on shared directional structure.