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I was reading how not to train your generative model paper. I don’t quite understand how the simplification from equation 4 to equation 5 can be right and based on my calculations it should be wrong. Would anyone mind giving me a hint? Specifically, if we assume $Q_{x_2}$ is independent of $x_1$ then this equation says that expectation of conditional KLs should equal the KL itself which I think is wrong. Am I making a mistake here? enter image description here

milad aghajohari
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