A real DDPM's Critical Boundary Detector correlates with LPIPS and localizes classifier-guidance-worthy timesteps

Sakamoto & Sakamoto define the Critical Boundary Detector (CBD), the Frobenius norm of the Jacobian of a diffusion model's own normalized score/velocity field along a single generation trajectory, and show on a real pretrained google/ddpm-cifar10-32 checkpoint that CBD correlates strongly with LPIPS perceptual distance (per-trajectory Pearson r of 0.953, 0.908, 0.966, 0.849 and 0.964 across 5 seeds, mean r=0.928, p<1e-70) [sakamoto-sakamoto-2026-geometry-phase-transitions-generative-dynamics-projection-caustics] Targeting classifier guidance to the CBD-detected instability band (timesteps 30-70 of 250) reaches target-class accuracy of 0.96-1.00 using only about 10 of 250 steps (roughly 4%), matching full 250-step guidance accuracy, while an equally-sized random band (timesteps 180-220) stays at the unguided baseline of 0.04 [sakamoto-sakamoto-2026-geometry-phase-transitions-generative-dynamics-projection-caustics] On real Stable Diffusion 3.5 Medium across 6 prompt-pairs (e.g. house-to-ship, jellyfish-to-chandelier), CBD-versus-LPIPS correlation is weaker and prompt-dependent (mean Pearson -0.230, mean Spearman -0.577, with per-prompt Spearman as strong as -0.993 for jellyfish-to-chandelier) [sakamoto-sakamoto-2026-geometry-phase-transitions-generative-dynamics-projection-caustics]