How does the reparameterization trick for variational autoencoders (VAE) work? Is there an intuitive and easy explanation without simplifying the underlying math? And why do we need the 'trick'? 
After reading through Kingma's NIPS 2015 workshop slides, I realized that we need the reparameterization trick in order to backpropagate through a random node.

Intuitively, in its original form, VAEs sample from a random node $z$ which is approximated by the parametric model $q(z \mid \phi, x)$ of the true posterior. Backprop cannot flow through a random node. 

Introducing a new parameter $\epsilon$ allows us to reparameterize $z$ in a way that allows backprop to flow through the deterministic nodes.


