Doesn't TensorFlow support random variables too? They even compare their performance to TensorFlow on a model with random variables.
The paper doesn't explain this well, but although you can put random variables in TensorFlow programs, you cannot backpropagate through them. With stochastic computation graphs, you can differentiate the expected loss as long as the probability density/mass functions of the random variables are differentiable. One of the main benefits of stochastic computation graphs is that you can train with arbitrary, non-differentiable simulators as long as they only depend on the parameters indirectly though random variables.
> They even compare their performance to TensorFlow on a model with random variables.
The naive variational autoencoder of Figure 2 cannot be trained in TensorFlow since the random variable depends on the parameters. However, this particular model can be reparameterized so that it doesn't depend on them without affecting the expected loss (Section 4.6) and the resulting model can be trained in TensorFlow.