tom:

But are you sure it is unexpected?
Does the VAE learn?
I do seem to recall that the loss could become negative in GPs, too, so there isn’t an inherent reason why it should not here


In my use case, the VAE learned stuff. As you mentioned above, this might indicate the normal distribution is very narrow/peaked (e.g. variances < 0.5). The log of small numbers becomes large (logvar_x) in the log-likelihood function and therefore that term dominates. At this point,  I think having a negative reconstruction is ok mathematically speaking but I still might be wrong.