Controlling Polar Exposure to Delay Memorization in Diffusion Models

Xuanchen Wang, Heng Wang, Weidong Cai

Diffusion models can reach useful sample quality before copying training examples, but fast optimization can compress this generalization window by accelerating sample-specific fitting. We investigate this effect through update geometry and propose Quality-Gated De-whitening (QGD), a controller that retains a fast polar-update prefix and progressively restores fixed-gain momentum. Our random-feature analysis separates covariance-controlled, curvature-equalized and amplitude-controlled memorization clocks. Under aligned spectral assumptions, it establishes a finite-exposure condition under which a fixed-gain tail recovers a delay proportional to dataset size. QGD implements this principle with a confirmed quality gate, a bounded decay envelope and causal copy feedback. Immediate switching is the conservative limit; gradual control balances delayed copying against continued quality improvement. We pair QGD with Copy-Budgeted Selection (CBS), which applies simultaneous binomial calibration to a frozen checkpoint family, followed by a fresh evaluation of the released checkpoint. On 2,000-image CIFAR-10 subsets, QGD preserves the polar baseline's quality-arrival time while expanding…