Alpha-bar is the cumulative product of alpha values: it tells you how much of the original signal remains after t diffusion steps. Alpha itself is the signal kept at one step, while alpha-bar combines every earlier retention rate. section 12.9
Following the retained signal
At step 1, alpha-bar is 0.99990. At step 2, it becomes 0.99990 × 0.99988 = 0.99978. At step 3, multiplying by 0.99986 gives 0.99964. Later steps therefore preserve progressively less original image information and replace more of it with noise. section 12.9
The value lets forward diffusion jump directly to a chosen timestep instead of repeatedly modifying the previous noisy image. The image combines scaled original pixels with scaled random noise: the signal scale uses √alpha-bar, and the noise scale uses √(1 − alpha-bar). section 12.9
