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For questions related to variational auto-encoders (VAEs). The first VAE was proposed in "Auto-Encoding Variational Bayes" (2013) by Diederik P. Kingma and Max Welling. There are several other VAEs, for example, the conditional VAE.

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How is this Pytorch expression equivalent to the KL divergence?

The code is correct. Since OP asked for a proof, one follows. The usage in the code is straightforward if you observe that the authors are using the symbols unconventionally: sigma is the natural loga …
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