Paper:
Iterative Refinement of the Approximate Posterior for Directed Belief Networks
Variational methods that rely on a recognition network to approximate the posterior of directed graphical models offer better inference and learning than previous methods. Recent advances that exploit the capacity and flexibility in this approach have expanded what kinds of models can be trained. However, as a proposal for the posterior, the capacity of the recognition network is limited, which can constrain the representational power of the generative model and increase the variance of Monte Carlo estimates. To address these issues, we introduce an iterative refinement procedure for improving the approximate posterior of the recognition network and show that training with the refined posterior is competitive with state-of-the-art methods. The advantages of refinement are further evident in an increased effective sample size, which implies a lower variance of gradient estimates.

Review:
This paper proposes a sequential Monte Carlo algorithm to improve posterior estimation in a class of generative models.  The main motivation is to reduce variance during training of autoencoder models that use discrete random variables in their latent space, which are unsuitable for standard variational autoencoder (VAE) training as they prevent the use of the so-called "reparametrization trick". Backpropagation through discrete stochastic unit is possible by using Monte Carlo gradient estimation, but these techniques tend to suffer from high estimation variance and hence poor convergence speed.  The proposed approach, iterative refinement for variational inference (IRVI), applies at each training step a sequential Monte Carlo algorithm to refine the posterior in order to reduce the estimation variance. The approach depends on the choice of a refinement procedure, which in the experiments reported in the paper is adaptive importance refinement (AIR).  The paper compares the proposed methods with other method described in the literature, including SOTA methods.
The paper is very clearly written and describes technical concepts in a very comprehensible way.  The approach is sound and well motivated and the experimental comparisons with other approaches are fair, though they could have been more extensive in terms of datasets.  My greatest concern is about the execution time of the proposed approach, since this is a sequential Monte Carlo method that performs multiple refinement passes for each step of the training process. The authors report convergence curves vs epochs but not vs wall clock time, which should be provided as the main motivation of the paper is to speed up training for this class of generative methods.  The experimental section is good in terms of which methods it compares against, but a bit lacking in terms of datasets. Comparisons on larger images and color images should be used. The paper reports SOTA or near SOTA likelihood, which is good, but it has been argued in the literature that this measure may not well correlate with subjective quality of generative models, hence larger and richer color image examples would be a valuable addition to the experimental section.  In conclusion I think that this paper provides a valuable contribution, it is well written well placed in comparison with existing approaches. It does however need some discussion and empirical evaluation of wall clock time complexity and it might use some more extensive choice of datasets in the experimental section.