Windowed Minority Guidance: Timestep-Localized Effects in Diffusion Denoising Dynamics

Minority guidance steers diffusion sampling toward under-represented data regions via a classifier gradient applied at every denoising step. We test whether this effect is timestep-localized by gating the gradient within fixed windows of the reverse chain and comparing the resulting classifier loss on the rarest of 100 minority-score buckets. Across a six-scale guidance sweep ($s \in \{0.5, 1.0, 2.0, 3.5, 5.0, 7.0\}$; 1500 paired-seed runs; LSUN Bedroom $256^2$), the middle third of the chain ($t \in [333, 667)$) recovers the largest share of the full-chain effect at every scale, rising from $\Delta_{\mathrm{rel}} = 0.456$ at $s = 0.5$ to $0.832$ at $s = 7.0$; its advantage over the late window is Bonferroni-significant only from $s \geq 2.0$. The early window improves over baseline on all 50 seeds at every scale, despite a small per-seed effect size. A finer 250-step sliding-window scan at $s = 3.5$ localizes the peak to $t \in [375, 625)$ ($\Delta_{\mathrm{rel}} = 0.536$), and the mid-window effect replicates tightly on an independent seed set ($0.693 \to 0.693$). We report the sweep, the sliding-window refinement, and two robustness checks (sample-size sensitivity, independent replication), and discuss why the relative-effect metric is denominator-sensitive and should be read as an association rather than a causal decomposition.