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This research investigates how perturbations introduced earlier in a diffusion sampling trajectory are amplified compared to fresh noise, revealing that "shaped" directions consistently yield larger endpoint changes than isotropic ones. The findings demonstrate that the magnitude of this amplification depends critically on the alignment between the perturbation and the specific latent trajectory, offering new insights into the dynamics of generative models.
Cross-Time Directional Selection in Diffusion Sampling
arXiv:2610.05199v1 Announce Type: new 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.
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.
12 pages, 6 figures. NeurIPS 2026 AI for Stochastic Dynamics Workshop (poster)
Machine Learning (cs.LG)
arXiv:2610.05199 [cs.LG]
(or arXiv:2610.05199v1 [cs.LG] for this version)
https://doi.org/10.48550/arXiv.2610.05199 Focus to learn more arXiv-issued DOI via DataCite (pending registration)
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