I’d like to know the answer as well. One thing that pops up is that VAEs use reparameterisation in order to avoid the autoencoder to learn the identity function, I’m not sure if neural processes suffer from the same problem (I haven’t read in detail)?
Another aspect is that VAEs are doing something like binary classification but on the distribution level not sure if neural process try to tackle the problem from the same perspective.
Finally, I’ve also encountered numerous papers that use the KL and FWIW I’m not fully convinced that empirically at least KL offers anything beyond what you’ll get with cross entropy.