Which generative model uses a 'reparameterization trick' to allow backpropagation through a stochastic latent variable?

Variational Autoencoder

Variational Autoencoders (VAEs) use this trick to separate the deterministic and stochastic parts of the latent variable. By expressing the latent sample as a deterministic function of the parameters and an independent noise variable, the gradient can flow back to the encoder.