  The variational autoencoder (VAE; Kingma, Welling (2014)) is a recently
proposed generative model pairing a top-down generative network with a
bottom-up recognition network which approximates posterior inference. It
typically makes strong assumptions about posterior inference, for instance that
the posterior distribution is approximately factorial, and that its parameters
can be approximated with nonlinear regression from the observations. As we show
empirically, the VAE objective can lead to overly simplified representations
which fail to use the network's entire modeling capacity. We present the
importance weighted autoencoder (IWAE), a generative model with the same
architecture as the VAE, but which uses a strictly tighter log-likelihood lower
bound derived from importance weighting. In the IWAE, the recognition network
uses multiple samples to approximate the posterior, giving it increased
flexibility to model complex posteriors which do not fit the VAE modeling
assumptions. We show empirically that IWAEs learn richer latent space
representations than VAEs, leading to improved test log-likelihood on density
estimation benchmarks.
