# Differentiable Annealed Importance Sampling Minimizes The Symmetrized Kullback-Leibler Divergence Between Initial and Target Distribution

arXiv: https://arxiv.org/abs/2405.14840 · HTML: https://mlsanity.com/paper/2405.14840/

## Key facts

- Cited by 2 papers in the map (data through 14 Oct 2026).
- Builds on 27 of its 48 references that are in the map.
- First posted on arXiv 23 May 2024.

## Builds on (most cited first, 27 of 27)

- [Variational Inference: A Review for Statisticians](https://mlsanity.com/paper/1601.00670/) (2016)
- [Importance Weighted Autoencoders](https://mlsanity.com/paper/1509.00519/) (2015)
- [Variational Continual Learning](https://mlsanity.com/paper/1710.10628/) (2017)
- [Black Box Variational Inference](https://mlsanity.com/paper/1401.0118/) (2013)
- [R'enyi Divergence Variational Inference](https://mlsanity.com/paper/1602.02311/) (2016)
- [Filtering Variational Objectives](https://mlsanity.com/paper/1705.09279/) (2017)
- [Importance Weighting and Variational Inference](https://mlsanity.com/paper/1808.09034/) (2018)
- [Score-Based Diffusion meets Annealed Importance Sampling](https://mlsanity.com/paper/2208.07698/) (2022)
- [Markovian Score Climbing: Variational Inference with KL(p||q)](https://mlsanity.com/paper/2003.10374/) (2020)
- [Hamiltonian Variational Auto-Encoder](https://mlsanity.com/paper/1805.11328/) (2018)
- [MCMC Variational Inference via Uncorrected Hamiltonian Annealing](https://mlsanity.com/paper/2107.04150/) (2021)
- [Black-box α-divergence Minimization](https://mlsanity.com/paper/1511.03243/) (2015)
- [Reinterpreting Importance-Weighted Autoencoders](https://mlsanity.com/paper/1704.02916/) (2017)
- [Monte Carlo Variational Auto-Encoders](https://mlsanity.com/paper/2106.15921/) (2021)
- [Differentiable Annealed Importance Sampling and the Perils of Gradient Noise](https://mlsanity.com/paper/2107.10211/) (2021)
- [Challenges and Opportunities in High-dimensional Variational Inference](https://mlsanity.com/paper/2103.01085/) (2021)
- [f-Divergence Variational Inference](https://mlsanity.com/paper/2009.13093/) (2020)
- [The Thermodynamic Variational Objective](https://mlsanity.com/paper/1907.00031/) (2019)
- [Langevin Diffusion Variational Inference](https://mlsanity.com/paper/2208.07743/) (2022)
- [A Contrastive Divergence for Combining Variational Inference and MCMC](https://mlsanity.com/paper/1905.04062/) (2019)
- [Variational Inference with Hamiltonian Monte Carlo](https://mlsanity.com/paper/1609.08203/) (2016)
- [Bayesian Evidence and Model Selection](https://mlsanity.com/paper/1411.3013/) (2014)
- [Improving Mutual Information Estimation with Annealed and Energy-Based Bounds](https://mlsanity.com/paper/2303.06992/) (2023)
- [Perturbative Black Box Variational Inference](https://mlsanity.com/paper/1709.07433/) (2017)
- [A Compact Representation for Bayesian Neural Networks By Removing Permutation Symmetry](https://mlsanity.com/paper/2401.00611/) (2023)
- [Markov Chain Score Ascent: A Unifying Framework of Variational Inference with Markovian Gradients](https://mlsanity.com/paper/2206.06295/) (2022)
- [Resampling Gradients Vanish in Differentiable Sequential Monte Carlo Samplers](https://mlsanity.com/paper/2304.14390/) (2023)

## Built on by (most cited first, 2 of 2)

- [Disentangling impact of capacity, objective, batchsize, estimators, and step-size on flow VI](https://mlsanity.com/paper/2412.08824/) (2024)
- [Asymptotically exact variational flows via involutive MCMC kernels](https://mlsanity.com/paper/2506.02162/) (2025)

## Abstract (arXiv)

Differentiable annealed importance sampling (DAIS), proposed by Geffner & Domke (2021) and Zhang et al. (2021), allows optimizing over the initial distribution of AIS. In this paper, we show that, in the limit of many transitions, DAIS minimizes the symmetrized Kullback-Leibler divergence between the initial and target distribution. Thus, DAIS can be seen as a form of variational inference (VI) as its initial distribution is a parametric fit to an intractable target distribution. We empirically evaluate the usefulness of the initial distribution as a variational distribution on synthetic and real-world data, observing that it often provides more accurate uncertainty estimates than VI (optimizing the reverse KL divergence), importance weighted VI, and Markovian score climbing (optimizing the forward KL divergence).