Research map / Probabilistic and scientific modeling / Variational and generative sampling
Importance sampling and quadrature
Reduces estimator variance using orthogonal Monte Carlo, annealing and control variates.
45 accepted papers at ICML, NeurIPS, ICLR, CVPR and AAAI (2016–2026) · an approach in Variational and generative sampling, keyword cluster “monte · carlo · mcmc”
State History Tried Preprints Who Export
Where it stands
Not enough benchmark data Fewer than four papers report the same benchmark, so there is no record to follow.
17 papers in 2023–24 and 10 in 2025–26 (at ICML, NeurIPS, ICLR, CVPR and AAAI); its share of the topic shrank, from 4.1% to 2.0%.
How this is decided
A benchmark is tracked when at least four papers of this approach report their own method on the same dataset and metric in at least two different years. Its record is the best number reported up to 2024 compared with the best reported in 2025–26: still improving means at least 1% better, flat means at most 0.2% better with at least two papers from 2025–26 trying. Numbers on a different scale from the rest (a fraction among percentages) and far outliers are left out. Results come from different papers with different setups, so they are signals, not head-to-head comparisons. The share of papers is counted at ICML, NeurIPS, ICLR, CVPR and AAAI.
How it got here
Most cited paper of each year
- 2016 · A Kernel Test of Goodness of Fit (ICML 2016 · 92 citations)
- 2017 · On the Sampling Problem for Kernel Quadrature (ICML 2017 · 5 citations)
- 2018 · On Nesting Monte Carlo Estimators (ICML 2018 · 35 citations)
- 2019 · Stein Point Markov Chain Monte Carlo (ICML 2019 · 20 citations)
- 2020 · Demystifying Orthogonal Monte Carlo and Beyond (NeurIPS 2020 · 5 citations)
- 2021 · Annealed Flow Transport Monte Carlo (ICML 2021 · 4 citations)
- 2022 · A Quadrature Rule combining Control Variates and Adaptive Importance Sampling (NeurIPS 2022 · 2 citations)
- 2023 · Vector-Valued Control Variates (ICML 2023 · 2 citations)
- 2024 · Principled Probabilistic Imaging using Diffusion Models as Plug-and-Play Priors (NeurIPS 2024 · 11 citations)
- 2025 · Nested Expectations with Kernel Quadrature (ICML 2025 · 0 citations)
- 2026 · Monte Carlo Diffusion for Generalizable Learning-Based RANSAC (AAAI 2026 · 1 citation)
Earliest papers here
- A Kernel Test of Goodness of Fit (ICML 2016 · 92 citations)
- Fast and Provably Good Seedings for k-Means (NeurIPS 2016 · 84 citations)
- Importance Sampling Tree for Large-scale Empirical Expectation (ICML 2016 · 16 citations)
What has been tried
34 papers here report 301 measured changes (a component added, removed or swapped, compared with a baseline): helped 67%, no clear effect 9%, hurt 19%, mixed 6%. Papers mostly publish changes that helped, so "helped" is over-represented.
Ablations in recent papers
| What was changed | Measured on | Result | Effect | Paper |
|---|---|---|---|---|
| Replace the VP diffusion prior with the VE diffusion prior | FFHQ validation, Gaussian deblur · PSNR | 29.46 -> 29.65 | Helped | Principled Probabilistic Imaging using Diffusion Models as Plug-and-Play Priors (NeurIPS 2024 · 11 citations) |
| Increase the NKQ regularization parameter substantially | Synthetic nested expectation · accuracy | Hurt | Nested Expectations with Kernel Quadrature (ICML 2025 · 0 citations) | |
| replace Tweedie's reconstruction with PF-ODE reconstruction | GMM (d_x=800, d_y=1), η=0.0 · sliced Wasserstein distance | 1.73±0.54 -> 1.37±0.43 | Helped | Solving Linear-Gaussian Bayesian Inverse Problems with Decoupled Diffusion Sequential Monte Carlo (ICML 2025 · 0 citations) |
| Increase sketch size from 100 to 1,900 probing vectors | fastMRI brain, E2E-VarNet, R=8, α=1 · NRMSE | Helped | Efficient Noise Calculation in Deep Learning-based MRI Reconstructions (ICML 2025 · 0 citations) | |
| Vary the denoising schedule among Standard, Geom(1,1), and Geom(2,1) | 8-Gaussians, Rings, Funnel, Sonar, Ionosphere · reported benchmark metric | Mixed | Stochastic Localization via Iterative Posterior Sampling (ICML 2024 · 0 citations) | |
| Add tempering to SMC | Source location · posterior estimation | 5\mathrm{e}^3 vs 10^6 | Helped | PASOA- PArticle baSed Bayesian Optimal Adaptive design (ICML 2024 · 0 citations) |
| Use ED-Bern rather than ED-Grid | NLL and MMD across synthetic datasets · NLL and MMD | Mixed | Energy-Based Modelling for Discrete and Mixed Data via Heat Equations on Structured Spaces (NeurIPS 2024 · 0 citations) |
Recent preprints
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Who publishes on it
Institutions on the most papers of this approach since 2023 (of 27 papers; from OpenAlex and the papers' affiliations).
- École Polytechnique · 3 papers
- Princeton University · 2 papers
- University of Cambridge · 2 papers
- University College London · 2 papers
- Inria · 2 papers
- New York University · 2 papers
Use it
Download BibTeX of 38 key papersOpen the topic in the interactive map
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Related approaches
Same keyword cluster
- Hamiltonian Monte Carlo (89 papers)
- Sequential Monte Carlo for inference (78 papers)
- Stochastic gradient MCMC (68 papers)
Elsewhere in the topic
- Likelihood-free and graphical model estimation (161 papers)
- Flow matching and flow sampling (144 papers)
- Posterior sampling with diffusion guidance (137 papers)
- Score-based generative modeling analysis (128 papers)
- Structured latent VAEs (125 papers)
- Exact inference for probabilistic programs (103 papers)
- Disentangled and discrete latent models (92 papers)
- Latent variable marginalization and estimators (91 papers)
Benchmark numbers, ablations and baseline numbers are extracted by AI from each paper's full text and can be wrong; the paper is the authority. Data: results index of 2026-11-02, citation counts from OpenAlex (2026-10-09).