Geometry of Phase Ordering in Diffusion and Flow
Abstract
We study same-state conditional prediction contrasts as descriptive measurements, separating the temporal concentration of prediction disagreement from terminal intervention response. The primary statistic is the appearance-minus-structural phase-center gap within a trained evaluating network. For three four-factor diffusion checkpoints, archived model-level summaries report a mean gap of (sample standard deviation ) on common trained trajectories, versus for untrained evaluators on the same states; this contrast is descriptive, not a causal estimate of training. A separate Gaussian-block calculation derives variance-dependent phase ordering for unnormalized population contrasts; in a learned-predictor test with five variance ratios, the reported non-null gaps have the predicted signs, whereas their magnitudes, the equal-variance control, and the archived peak positions disagree with the prediction. In SD3.5 Medium, static directions attain the same reported classification accuracy as aligned updates, and text-only features classify 24/24 queries versus 23/24. In an onset audit, eight of 18 cases pass the archived primary gate flags, the geometry-peak error is 1.375 steps versus 1.25 for a fixed-step predictor, and a routing pilot does not establish an advantage. We therefore distinguish the reported phase organization from mechanistic identification, calibrated onset prediction, and verified-budget control utility.
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