# Why the intermediate steps of a diffusion model (q(xt|xt-1)) can be considered as a Conditional Gaussian Distribution?

I have a similar doubt to this question: Why can de-noising diffusion models be sampled with Gaussian distributions?

As asked in the original question, when we start from xo (the original image) and add gaussian noise to it, then why is x1 and every subsequent noisy image sample modelled to be coming from a conditional gaussian distribution? That is, how does q(x0) + Gaussian noise result in a q(x1|x0) being a Gaussian distribution? Do they implicitly assume the original data distribution to be Gaussian? PS: I know continuous addition of Gaussian noise to xo will result in a pure gaussian noise at time = T (T tending to infinity), i.e, q(xT|x0) (when a lot of noise has been added), but what concerns me is using the Gaussian distribution for modelling the intermediate steps q(x1|xo). Thank you for your help.

Please refer to Equation 2 of Equation 2 of https://arxiv.org/pdf/2006.11239.pdf