  Media is generally stored digitally and is therefore discrete. Many
successful deep distribution models in deep learning learn a density, i.e., the
distribution of a continuous random variable. Na\"ive optimization on discrete
data leads to arbitrarily high likelihoods, and instead, it has become standard
practice to add noise to datapoints. In this paper, we present a general
framework for dequantization that captures existing methods as a special case.
We derive two new dequantization objectives: importance-weighted (iw)
dequantization and R\'enyi dequantization. In addition, we introduce
autoregressive dequantization (ARD) for more flexible dequantization
distributions. Empirically we find that iw and R\'enyi dequantization
considerably improve performance for uniform dequantization distributions. ARD
achieves a negative log-likelihood of 3.06 bits per dimension on CIFAR10, which
to the best of our knowledge is state-of-the-art among distribution models that
do not require autoregressive inverses for sampling.
