Early Semantic Commitment in Diffusion Sampling

Patrick Reichherzer

Keywords: diffusion models, DDIM, semantic commitment, score Jacobian, Fisher geometry, Mahalanobis analysis

TL;DR: The earliest outcome-conditioned signal in diffusion sampling lives in the denoiser's clean-sample response, not in state-space trajectory divergence

Abstract: When do diffusion trajectories first reveal their final semantic outcome? Prior work mainly studies population-level transitions, while nearby seeds can still end in different semantic basins. We introduce Trajectory Sensitivity Analysis (TSA): pair nearby noise seeds, run deterministic DDIM, and condition trajectory statistics on whether final outputs are semantically stable or flipped. State-space RMSE separates flip and stable pairs only around $\bar\alpha_t\sim10^{-2}$. This is a delayed signature. An earlier cohort-level signal appears in the denoiser's clean-sample prediction as a transverse secant defect at $\bar\alpha_t\approx1.7\times10^{-4}$, about 60 times earlier in signal fraction than the state-space onset. Pairwise predictability emerges later: a leave-seed-out probe becomes useful at larger signal fractions, and its AUC trajectory is predicted by a plug-in Mahalanobis/LDA calculation with RMS residual $0.012$. TSA separates visual separability, cohort-level semantic structure, and per-pair predictability, locating the first outcome-conditioned signal in clean-sample response.

Submission Number: 226