  This paper considers the problem of lossy neural image compression (NIC).
Current state-of-the-art (sota) methods adopt uniform posterior to approximate
quantization noise, and single-sample pathwise estimator to approximate the
gradient of evidence lower bound (ELBO). In this paper, we propose to train NIC
with multiple-sample importance weighted autoencoder (IWAE) target, which is
tighter than ELBO and converges to log likelihood as sample size increases.
First, we identify that the uniform posterior of NIC has special properties,
which affect the variance and bias of pathwise and score function estimators of
the IWAE target. Moreover, we provide insights on a commonly adopted trick in
NIC from gradient variance perspective. Based on those analysis, we further
propose multiple-sample NIC (MS-NIC), an enhanced IWAE target for NIC.
Experimental results demonstrate that it improves sota NIC methods. Our MS-NIC
is plug-and-play, and can be easily extended to other neural compression tasks.
