[Discussion] Struggling with a derivation in the diffusion probabilistic model paper

Can someone help me figure out the error in my derivation from the paper, Deep Unsupervised Learning using Nonequilibrium Thermodynamics" (2015): [https://arxiv.org/pdf/1503.03585.pdf](https://arxiv.org/pdf/1503.03585.pdf)

I have posted the full question on AI stack exchange in the link below:

[https://ai.stackexchange.com/questions/45272/trying-to-understand-some-derivation-in-the-paper-deep-unsupervised-learning-us](https://ai.stackexchange.com/questions/45272/trying-to-understand-some-derivation-in-the-paper-deep-unsupervised-learning-us)

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