  Denoising autoencoders (DAE) are trained to reconstruct their clean inputs
with noise injected at the input level, while variational autoencoders (VAE)
are trained with noise injected in their stochastic hidden layer, with a
regularizer that encourages this noise injection. In this paper, we show that
injecting noise both in input and in the stochastic hidden layer can be
advantageous and we propose a modified variational lower bound as an improved
objective function in this setup. When input is corrupted, then the standard
VAE lower bound involves marginalizing the encoder conditional distribution
over the input noise, which makes the training criterion intractable. Instead,
we propose a modified training criterion which corresponds to a tractable bound
when input is corrupted. Experimentally, we find that the proposed denoising
variational autoencoder (DVAE) yields better average log-likelihood than the
VAE and the importance weighted autoencoder on the MNIST and Frey Face
datasets.
