Learning goal: at a chosen time, xt = √ᾱt x0 + σt ε is scaled clean data plus Gaussian noise. The intermediate signal/noise balance is set by the schedule schedule.

Point cloud: current x t; colors interpolate between data and noise.

Curves: ᾱ t for signal variance and 1−ᾱ t for noise variance; marker: current t.

t = 0 / 1000 √ᾱt = 1.000 σt = 0.000 SNR = ∞

Move t forward: structure becomes noisier and approaches N(0,I). Changing the schedule alters the intermediate rate of signal loss. Finite discrete endpoints need not be exactly pure noise; the schedule and training objective affect practical behavior.