  This paper introduces novel results for the score function gradient estimator
of the importance weighted variational bound (IWAE). We prove that in the limit
of large $K$ (number of importance samples) one can choose the control variate
such that the Signal-to-Noise ratio (SNR) of the estimator grows as $\sqrt{K}$.
This is in contrast to the standard pathwise gradient estimator where the SNR
decreases as $1/\sqrt{K}$. Based on our theoretical findings we develop a novel
control variate that extends on VIMCO. Empirically, for the training of both
continuous and discrete generative models, the proposed method yields superior
variance reduction, resulting in an SNR for IWAE that increases with $K$
without relying on the reparameterization trick. The novel estimator is
competitive with state-of-the-art reparameterization-free gradient estimators
such as Reweighted Wake-Sleep (RWS) and the thermodynamic variational objective
(TVO) when training generative models.
