mlsanityData to 14 Oct 2026

MCMC Variational Inference via Uncorrected Hamiltonian Annealing

arXiv 2107.04150 ↗First posted 8 Jul 2021cs.LG stat.MLcited by 39

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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.

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

24 of 62 references.

References · 24

  1. 2014Adam: A Method for Stochastic Optimizationcited by 37,240
  2. 2013Auto-Encoding Variational Bayescited by 4,053
  3. 2015Variational Inference with Normalizing Flowscited by 2,170
  4. 2016Variational Inference: A Review for Statisticianscited by 1,472
  5. 2015Importance Weighted Autoencoderscited by 456
  6. 2018Deep Learning for Classical Japanese Literaturecited by 422
  7. 2014Stochastic Gradient Hamiltonian Monte Carlocited by 343
  8. 2017Advances in Variational Inferencecited by 236
  9. 2017Underdamped Langevin MCMC: A non-asymptotic analysiscited by 133
  10. 2018Importance Weighting and Variational Inferencecited by 55
  11. 2018Hamiltonian Variational Auto-Encodercited by 41
  12. 2018Doubly Reparameterized Gradient Estimators for Monte Carlo Objectivescited by 41
12 more
  1. 2016On the Quantitative Analysis of Decoder-Based Generative Modelscited by 40
  2. 2017Reinterpreting Importance-Weighted Autoencoderscited by 37
  3. 2021Monte Carlo Variational Auto-Encoderscited by 36
  4. 2018Improving Explorability in Variational Inference with Annealed Variational Objectivescited by 24
  5. 2017Approximate Inference with Amortised MCMCcited by 23
  6. 2019A Contrastive Divergence for Combining Variational Inference and MCMCcited by 21
  7. 2015Sandwiching the marginal likelihood using bidirectional Monte Carlocited by 20
  8. 2014The Geometric Foundations of Hamiltonian Monte Carlocited by 19
  9. 2016Variational Inference with Hamiltonian Monte Carlocited by 17
  10. 2019Divide and Couple: Using Monte Carlo Variational Objectives for Posterior Approximationcited by 14
  11. 2016Measuring the reliability of MCMC inference with bidirectional Monte Carlocited by 8
  12. 2019Learning Deep Generative Models with Annealed Importance Samplingcited by 8

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Cited by year (2026 to 14 Oct)

Citing papers per year: 2021: 3; 2022: 9; 2023: 8; 2024: 8; 2025: 10; 2026: 1.

39 papers.

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  1. 2023Reduce, Reuse, Recycle: Compositional Generation with Energy-Based Diffusion Models and MCMCcited by 220
  2. 2023Denoising Diffusion Samplerscited by 149
  3. 2022Flow Annealed Importance Sampling Bootstrapcited by 127
  4. 2024Iterated Denoising Energy Matching for Sampling from Boltzmann Densitiescited by 116
  5. 2022Continual Repeated Annealed Flow Transport Monte Carlocited by 66
  6. 2024Beyond ELBOs: A Large-Scale Evaluation of Variational Methods for Samplingcited by 56
  7. 2022Score-Based Diffusion meets Annealed Importance Samplingcited by 51
  8. 2024Sequential Controlled Langevin Diffusionscited by 48
  9. 2021Differentiable Annealed Importance Sampling and the Perils of Gradient Noisecited by 36
  10. 2025Underdamped Diffusion Bridges with Applications to Samplingcited by 29
  11. 2022Langevin Diffusion Variational Inferencecited by 26
  12. 2024Liouville Flow Importance Samplercited by 25
27 more
  1. 2021Generalized Normalizing Flows via Markov Chainscited by 23
  2. 2025Trust Region Constrained Measure Transport in Path Space for Stochastic Optimal Control and Inferencecited by 23
  3. 2023Transport meets Variational Inference: Controlled Monte Carlo Diffusionscited by 21
  4. 2025Proximal Diffusion Neural Samplercited by 16
  5. 2021Surrogate Likelihoods for Variational Annealed Importance Samplingcited by 14
  6. 2022Bayesian inference via sparse Hamiltonian flowscited by 12
  7. 2022MixFlows: principled variational inference via mixed flowscited by 11
  8. 2024Learned Reference-based Diffusion Sampling for multi-modal distributionscited by 9
  9. 2025Non-equilibrium Annealed Adjoint Samplercited by 8
  10. 2023Adaptive Annealed Importance Sampling with Constant Rate Progresscited by 7
  11. 2023MCMC-Correction of Score-Based Diffusion Models for Model Compositioncited by 7
  12. 2022Markov Chain Score Ascent: A Unifying Framework of Variational Inference with Markovian Gradientscited by 6
  13. 2023Embracing the chaos: analysis and diagnosis of numerical instability in variational flowscited by 6
  14. 2025Neural Flow Samplers with Shortcut Modelscited by 5
  15. 2022Variational Inference with Locally Enhanced Bounds for Hierarchical Modelscited by 4
  16. 2025End-To-End Learning of Gaussian Mixture Priors for Diffusion Samplercited by 4
  17. 2023Resampling Gradients Vanish in Differentiable Sequential Monte Carlo Samplerscited by 2
  18. 2023Reparameterized Variational Rejection Samplingcited by 2
  19. 2024Differentiable Annealed Importance Sampling Minimizes The Symmetrized Kullback-Leibler Divergence Between Initial and Target Distributioncited by 2
  20. 2025Importance Weighted Score Matching for Diffusion Samplers with Enhanced Mode Coveragecited by 2
  21. 2022Optimization of Annealed Importance Sampling Hyperparameterscited by 1
  22. 2025Bayesian Computation in Deep Learningcited by 1
  23. 2025Asymptotically exact variational flows via involutive MCMC kernelscited by 1
  24. 2025Continuously Tempered Diffusion Samplerscited by 1
  25. 2024MCMC-driven learningcited by 0
  26. 2024Feynman-Kac Operator Expectation Estimatorcited by 0
  27. 2026Large-scale empirical tuning and comparison of default optimizers for variational inferencecited by 0