# Sequential Monte Carlo for Inclusive KL Minimization in Amortized Variational Inference

arXiv: https://arxiv.org/abs/2403.10610 · HTML: https://mlsanity.com/paper/2403.10610/

## Key facts

- Cited by 7 papers in the map (data through 14 Oct 2026).
- Builds on 19 of its 46 references that are in the map.
- First posted on arXiv 15 Mar 2024.

## Builds on (most cited first, 19 of 19)

- [Variational Inference: A Review for Statisticians](https://mlsanity.com/paper/1601.00670/) (2016)
- [Neural Spline Flows](https://mlsanity.com/paper/1906.04032/) (2019)
- [Black Box Variational Inference](https://mlsanity.com/paper/1401.0118/) (2013)
- [Automatic Posterior Transformation for Likelihood-Free Inference](https://mlsanity.com/paper/1905.07488/) (2019)
- [Benchmarking Simulation-Based Inference](https://mlsanity.com/paper/2101.04653/) (2021)
- [Inference Suboptimality in Variational Autoencoders](https://mlsanity.com/paper/1801.03558/) (2018)
- [Variational Sequential Monte Carlo](https://mlsanity.com/paper/1705.11140/) (2017)
- [Filtering Variational Objectives](https://mlsanity.com/paper/1705.09279/) (2017)
- [Annealed Flow Transport Monte Carlo](https://mlsanity.com/paper/2102.07501/) (2021)
- [Reweighted Wake-Sleep](https://mlsanity.com/paper/1406.2751/) (2014)
- [Continual Repeated Annealed Flow Transport Monte Carlo](https://mlsanity.com/paper/2201.13117/) (2022)
- [Auto-Encoding Sequential Monte Carlo](https://mlsanity.com/paper/1705.10306/) (2017)
- [Elements of Sequential Monte Carlo](https://mlsanity.com/paper/1903.04797/) (2019)
- [Importance Weighting and Variational Inference](https://mlsanity.com/paper/1808.09034/) (2018)
- [Markovian Score Climbing: Variational Inference with KL(p||q)](https://mlsanity.com/paper/2003.10374/) (2020)
- [Neural Adaptive Sequential Monte Carlo](https://mlsanity.com/paper/1506.03338/) (2015)
- [Differentiable Particle Filtering without Modifying the Forward Pass](https://mlsanity.com/paper/2106.10314/) (2021)
- [Forward Amortized Inference for Likelihood-Free Variational Marginalization](https://mlsanity.com/paper/1805.11542/) (2018)
- [Nested Variational Inference](https://mlsanity.com/paper/2106.11302/) (2021)

## Built on by (most cited first, 7 of 7)

- [Do-PFN: In-Context Learning for Causal Effect Estimation](https://mlsanity.com/paper/2506.06039/) (2025)
- [Inclusive KL Gradient Flows: Otto-Wasserstein, Fisher-Rao-Gaussian, and Local-Estimator Dynamics](https://mlsanity.com/paper/2411.00214/) (2024)
- [Globally Convergent Variational Inference](https://mlsanity.com/paper/2501.08201/) (2025)
- [Control, Optimal Transport and Neural Differential Equations in Supervised Learning](https://mlsanity.com/paper/2503.15105/) (2025)
- [Global Variational Inference Enhanced Robust Domain Adaptation](https://mlsanity.com/paper/2507.03291/) (2025)
- [Efficient Inference for Coupled Hidden Markov Models in Continuous Time and Discrete Space](https://mlsanity.com/paper/2510.12916/) (2025)
- [Beyond Global Divergences: A Local-Mass Perspective on Bayesian Inference](https://mlsanity.com/paper/2606.27090/) (2026)

## Abstract (arXiv)

For training an encoder network to perform amortized variational inference, the Kullback-Leibler (KL) divergence from the exact posterior to its approximation, known as the inclusive or forward KL, is an increasingly popular choice of variational objective due to the mass-covering property of its minimizer. However, minimizing this objective is challenging. A popular existing approach, Reweighted Wake-Sleep (RWS), suffers from heavily biased gradients and a circular pathology that results in highly concentrated variational distributions. As an alternative, we propose SMC-Wake, a procedure for fitting an amortized variational approximation that uses likelihood-tempered sequential Monte Carlo samplers to estimate the gradient of the inclusive KL divergence. We propose three gradient estimators, all of which are asymptotically unbiased in the number of iterations and two of which are strongly consistent. Our method interleaves stochastic gradient updates, SMC samplers, and iterative improvement to an estimate of the normalizing constant to reduce bias from self-normalization. In experiments with both simulated and real datasets, SMC-Wake fits variational distributions that approximate the posterior more accurately than existing methods.