I was reading this paper, "An Edit Friendly DDPM Noise Space: Inversion and Manipulations". In page no. 4, they have mentioned that in DDPM, noise maps of consecutive steps are highly correlated while their edit friendly noise maps of consecutive steps are independent.
How are the noise maps in DDPM highly correlated? I couldn't figure out the difference in their noise maps and in those of native DDPM. I understand that xt and xt-1 can have high or low variance depending on the value of alpha, but how will epsilon of consecutive steps have high or low variance when they are being randomly sampled from unit normal distribution.
Also, in abstract, they have mentioned complete opposite thing, "As opposed to the native DDPM noise space, the edit-friendly noise maps do not have a standard normal distribution and are not statistically independent across timesteps."
Am I missing something or is there some mistake in my understanding?