Cross-Time Directional Selection in Diffusion Sampling

Dhia naouali

cs.LGOct 4, 2026

Cross-Time Directional Selection in Diffusion Sampling

Authors: Dhia naouali

Organizations: Independent Researcher

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.

Figures & tables

Figure 1: Matched replay tests cross-time directional selection. (A) We transport a perturbation from

a

b

to obtain an upstream-shaped direction. We then replay this direction and a fresh Gaussian direction at equal RMS magnitude around the same unperturbed late state

z_{b}

, and pass both through the same remaining updates. (B) Median paired shaped-to-fresh endpoint angular-gain ratios, shown for each sampler and source time.

Model	Fresh	Shaped from 5	Shaped from 20	Shaped from 35
SiT-XL/2	0.816	1.202 (1.496 $\times$ )	1.132 (1.409 $\times$ )	0.927 (1.138 $\times$ )
DiT-XL/2	0.766	1.725 (2.350 $\times$ )	1.638 (2.214 $\times$ )	1.017 (1.330 $\times$ )
LightningDiT-XL/1	0.560	1.096 (1.969 $\times$ )	0.908 (1.623 $\times$ )	0.660 (1.179 $\times$ )

Table 1: Median endpoint angular gain. Parentheses give the median trajectory-level shaped-to-fresh gain ratio. Each entry summarizes 1,024 trajectories with two probe axes per trajectory.

Response	Shaped from 5	Shaped from 20	Shaped from 35
Pixel RMS	1.007	0.959	0.964
DINOv2 CLS	1.264	1.116	0.999
DINOv2 mean patch	1.256	1.156	1.017
ResNet-50	1.135	1.066	0.990

Table 2: Shaped-to-fresh response ratios after equal-RMS endpoint replay in SiT. Values are medians across 256 trajectories after geometrically combining the two axis-wise ratios within each trajectory. Values above one indicate a larger response to the shaped direction.

Appendix figures & tables9 assets

Supplementary material from the paper’s appendix.

Appendix

Figure 2: Finite-radius control in SiT. On a separate 256-trajectory cohort, the median paired shaped-to-fresh endpoint angular-gain ratio changes by at most 0.0004 across the eightfold replay-radius range, with the source radius fixed.

Model	Fresh	Source 5	Source 20	Source 35
SiT-XL/2	0.952	1.403	1.324	1.083
DiT-XL/2	0.723	1.627	1.540	0.953
LightningDiT-XL/1	0.668	1.307	1.084	0.786

Appendix

Table 3: Median endpoint latent-RMS gain under matched replay. The shaped-over-fresh ordering agrees with Table 1 , although angular and latent-RMS gain can fall on opposite sides of one.

Model	Source	Own/fresh	Own/within	Own/across
SiT	5	1.509 (1.468–1.531)	1.413 (1.388–1.447)	1.410 (1.381–1.447)
SiT	20	1.413 (1.390–1.444)	1.357 (1.329–1.381)	1.354 (1.329–1.383)
SiT	35	1.141 (1.134–1.151)	1.121 (1.111–1.131)	1.121 (1.114–1.130)
DiT	5	2.353 (2.279–2.504)	2.004 (1.906–2.094)	2.001 (1.913–2.105)
DiT	20	2.255 (2.192–2.379)	2.050 (1.922–2.141)	2.017 (1.942–2.114)
DiT	35	1.337 (1.323–1.364)	1.284 (1.270–1.313)	1.293 (1.273–1.325)

Appendix

Table 4: Median paired endpoint angular-gain ratios for donor replay. Parentheses give 95% class-block bootstrap intervals.

Model	Largest absolute change in median paired ratio
SiT	0.007%
DiT	0.008%
LightningDiT	0.004%

Appendix

Table 5: Stability of the paired angular-gain ratio under source-radius variation.

Model	Source 5	Source 20	Source 35
SiT	[1.482, 1.515]	[1.399, 1.421]	[1.133, 1.142]
DiT	[2.290, 2.409]	[2.153, 2.259]	[1.322, 1.342]
LightningDiT	[1.951, 1.983]	[1.609, 1.635]	[1.176, 1.181]

Appendix

Table 6: Paired trajectory bootstrap intervals for the main comparison. Entries are 95% intervals for the median shaped-to-fresh endpoint angular-gain ratios in Table 1 , based on 10,000 draws.

Figure 3: Equal-RMS endpoint replay produces different feature responses. (A) Median shaped-to-fresh response ratios after replaying both directions at equal RMS magnitude around the same endpoint state. (B) Fraction of matched axis pairs for which the shaped response exceeds the fresh response.

Figure 4: Timing association in SiT. Fresh-probe crossover time and angular-speed peak time co-vary across 256 trajectories, with contraction typically preceding peak angular motion.

Figure 5: Alignment and angular motion capture different aspects of sampling. (A) Median alignment between each latent state and its endpoint increases smoothly. (B) Median angular speed of the latent state direction is non-monotonic and peaks at a model-dependent time. Shading denotes the interquartile range across 1,024 trajectories per model.

Figure 6: Token norm and local gain in SiT. Pre-perturbation token norm has little consistent association with fresh, reset-shaped, or transported endpoint gain.

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Recent work has popularized a practical recipe in diffusion and flow matching: predict the clean signal

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Abstract

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