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ddpm-cifar10-32

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Hi,

exists any proof for these equations?

I understand it as condition probability with multiple conditions, that is defined as:

x_0 is as I understand from real data distribution that could not be Gaussian.
x_t is a combination of x_0 distribution and Gaussian distribution parametrised by β_t.

Similarly in the DDIM is not the proof behind the mean and variance definition:

Thanks.