# MCMC Variational Inference via Uncorrected Hamiltonian Annealing

arXiv: https://arxiv.org/abs/2107.04150 · HTML: https://mlsanity.com/paper/2107.04150/

## Key facts

- Cited by 39 papers in the map (data through 14 Oct 2026).
- Builds on 24 of its 62 references that are in the map.
- First posted on arXiv 8 Jul 2021.

## Builds on (most cited first, 24 of 24)

- [Adam: A Method for Stochastic Optimization](https://mlsanity.com/paper/1412.6980/) (2014)
- [Auto-Encoding Variational Bayes](https://mlsanity.com/paper/1312.6114/) (2013)
- [Variational Inference with Normalizing Flows](https://mlsanity.com/paper/1505.05770/) (2015)
- [Variational Inference: A Review for Statisticians](https://mlsanity.com/paper/1601.00670/) (2016)
- [Importance Weighted Autoencoders](https://mlsanity.com/paper/1509.00519/) (2015)
- [Deep Learning for Classical Japanese Literature](https://mlsanity.com/paper/1812.01718/) (2018)
- [Stochastic Gradient Hamiltonian Monte Carlo](https://mlsanity.com/paper/1402.4102/) (2014)
- [Advances in Variational Inference](https://mlsanity.com/paper/1711.05597/) (2017)
- [Underdamped Langevin MCMC: A non-asymptotic analysis](https://mlsanity.com/paper/1707.03663/) (2017)
- [Importance Weighting and Variational Inference](https://mlsanity.com/paper/1808.09034/) (2018)
- [Hamiltonian Variational Auto-Encoder](https://mlsanity.com/paper/1805.11328/) (2018)
- [Doubly Reparameterized Gradient Estimators for Monte Carlo Objectives](https://mlsanity.com/paper/1810.04152/) (2018)
- [On the Quantitative Analysis of Decoder-Based Generative Models](https://mlsanity.com/paper/1611.04273/) (2016)
- [Reinterpreting Importance-Weighted Autoencoders](https://mlsanity.com/paper/1704.02916/) (2017)
- [Monte Carlo Variational Auto-Encoders](https://mlsanity.com/paper/2106.15921/) (2021)
- [Improving Explorability in Variational Inference with Annealed Variational Objectives](https://mlsanity.com/paper/1809.01818/) (2018)
- [Approximate Inference with Amortised MCMC](https://mlsanity.com/paper/1702.08343/) (2017)
- [A Contrastive Divergence for Combining Variational Inference and MCMC](https://mlsanity.com/paper/1905.04062/) (2019)
- [Sandwiching the marginal likelihood using bidirectional Monte Carlo](https://mlsanity.com/paper/1511.02543/) (2015)
- [The Geometric Foundations of Hamiltonian Monte Carlo](https://mlsanity.com/paper/1410.5110/) (2014)
- [Variational Inference with Hamiltonian Monte Carlo](https://mlsanity.com/paper/1609.08203/) (2016)
- [Divide and Couple: Using Monte Carlo Variational Objectives for Posterior Approximation](https://mlsanity.com/paper/1906.10115/) (2019)
- [Measuring the reliability of MCMC inference with bidirectional Monte Carlo](https://mlsanity.com/paper/1606.02275/) (2016)
- [Learning Deep Generative Models with Annealed Importance Sampling](https://mlsanity.com/paper/1906.04904/) (2019)

## Built on by (most cited first, 30 of 39)

- [Reduce, Reuse, Recycle: Compositional Generation with Energy-Based Diffusion Models and MCMC](https://mlsanity.com/paper/2302.11552/) (2023)
- [Denoising Diffusion Samplers](https://mlsanity.com/paper/2302.13834/) (2023)
- [Flow Annealed Importance Sampling Bootstrap](https://mlsanity.com/paper/2208.01893/) (2022)
- [Iterated Denoising Energy Matching for Sampling from Boltzmann Densities](https://mlsanity.com/paper/2402.06121/) (2024)
- [Continual Repeated Annealed Flow Transport Monte Carlo](https://mlsanity.com/paper/2201.13117/) (2022)
- [Beyond ELBOs: A Large-Scale Evaluation of Variational Methods for Sampling](https://mlsanity.com/paper/2406.07423/) (2024)
- [Score-Based Diffusion meets Annealed Importance Sampling](https://mlsanity.com/paper/2208.07698/) (2022)
- [Sequential Controlled Langevin Diffusions](https://mlsanity.com/paper/2412.07081/) (2024)
- [Differentiable Annealed Importance Sampling and the Perils of Gradient Noise](https://mlsanity.com/paper/2107.10211/) (2021)
- [Underdamped Diffusion Bridges with Applications to Sampling](https://mlsanity.com/paper/2503.01006/) (2025)
- [Langevin Diffusion Variational Inference](https://mlsanity.com/paper/2208.07743/) (2022)
- [Liouville Flow Importance Sampler](https://mlsanity.com/paper/2405.06672/) (2024)
- [Generalized Normalizing Flows via Markov Chains](https://mlsanity.com/paper/2111.12506/) (2021)
- [Trust Region Constrained Measure Transport in Path Space for Stochastic Optimal Control and Inference](https://mlsanity.com/paper/2508.12511/) (2025)
- [Transport meets Variational Inference: Controlled Monte Carlo Diffusions](https://mlsanity.com/paper/2307.01050/) (2023)
- [Proximal Diffusion Neural Sampler](https://mlsanity.com/paper/2510.03824/) (2025)
- [Surrogate Likelihoods for Variational Annealed Importance Sampling](https://mlsanity.com/paper/2112.12194/) (2021)
- [Bayesian inference via sparse Hamiltonian flows](https://mlsanity.com/paper/2203.05723/) (2022)
- [MixFlows: principled variational inference via mixed flows](https://mlsanity.com/paper/2205.07475/) (2022)
- [Learned Reference-based Diffusion Sampling for multi-modal distributions](https://mlsanity.com/paper/2410.19449/) (2024)
- [Non-equilibrium Annealed Adjoint Sampler](https://mlsanity.com/paper/2506.18165/) (2025)
- [Adaptive Annealed Importance Sampling with Constant Rate Progress](https://mlsanity.com/paper/2306.15283/) (2023)
- [MCMC-Correction of Score-Based Diffusion Models for Model Composition](https://mlsanity.com/paper/2307.14012/) (2023)
- [Markov Chain Score Ascent: A Unifying Framework of Variational Inference with Markovian Gradients](https://mlsanity.com/paper/2206.06295/) (2022)
- [Embracing the chaos: analysis and diagnosis of numerical instability in variational flows](https://mlsanity.com/paper/2307.06957/) (2023)
- [Neural Flow Samplers with Shortcut Models](https://mlsanity.com/paper/2502.07337/) (2025)
- [Variational Inference with Locally Enhanced Bounds for Hierarchical Models](https://mlsanity.com/paper/2203.04432/) (2022)
- [End-To-End Learning of Gaussian Mixture Priors for Diffusion Sampler](https://mlsanity.com/paper/2503.00524/) (2025)
- [Resampling Gradients Vanish in Differentiable Sequential Monte Carlo Samplers](https://mlsanity.com/paper/2304.14390/) (2023)
- [Reparameterized Variational Rejection Sampling](https://mlsanity.com/paper/2309.14612/) (2023)

## Abstract (arXiv)

Given an unnormalized target distribution we want to obtain approximate samples from it and a tight lower bound on its (log) normalization constant log Z. Annealed Importance Sampling (AIS) with Hamiltonian MCMC is a powerful method that can be used to do this. Its main drawback is that it uses non-differentiable transition kernels, which makes tuning its many parameters hard. We propose a framework to use an AIS-like procedure with Uncorrected Hamiltonian MCMC, called Uncorrected Hamiltonian Annealing. Our method leads to tight and differentiable lower bounds on log Z. We show empirically that our method yields better performances than other competing approaches, and that the ability to tune its parameters using reparameterization gradients may lead to large performance improvements.