Query about the KL divergence calculation with RNF about wae-rnf-lm HOT 2 CLOSED

Hi @vikigenius , this is a good question. Thanks for asking.

The naming is a little misleading. flow_kld measures the KL divergence between q(z_T|x) and p(z_T), which is not the KL you listed from the loss function. The KL you mentioned is based on q(z_0|x) and p(z_T). Using flow_kld in loss function is not correct. To see why, here is a complete derivation,

In short, once you apply normalizing flow, and you include the summation of log Jacobian in your loss function, then the posterior in KL should be q(z_0|x) rather than q(z_T|x). The same derivation can also be found in other normalizing flow papers.

Let me know if this answers your question. Thanks again!

from wae-rnf-lm.

Thanks for the clear derivation, now it's clear.

from wae-rnf-lm.