Research map / Probabilistic and scientific modeling / Variational and generative sampling
Posterior sampling with diffusion guidance
Samples posteriors or unnormalized targets using gradient flows, Stein guidance and amortized samplers.
137 accepted papers at ICML, NeurIPS, ICLR, CVPR and AAAI (2016–2026) · an approach in Variational and generative sampling, keyword cluster “diffusion · score · matching”
State History Benchmarks Tried Baselines Checklist Preprints Who Export
Where it stands
Few recent reports The tracked benchmarks have at most one report from 2025–26 that could beat the old record, too few to say whether they are still moving.
28 papers in 2023–24 and 54 in 2025–26 (at ICML, NeurIPS, ICLR, CVPR and AAAI); its share of the topic grew, from 6.8% to 10.8%.
Open questions the data points to
- Papers report DCGAN on CelebA (FID) anywhere from 12.5 to 52.5: comparisons against it depend on whose number you take.
- Papers report VAE on CelebA (FID) anywhere from 38.76 to 79.09: comparisons against it depend on whose number you take.
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 · Deep Structured Energy Based Models for Anomaly Detection (ICML 2016 · 249 citations)
- 2017 · Ensemble Sampling (NeurIPS 2017 · 46 citations)
- 2018 · Large Scale Optimal Transport and Mapping Estimation (ICLR 2018 · 73 citations)
- 2019 · Overcoming Limitations of Mixture Density Networks: A Sampling and Fitting Framework for Multimodal Future Prediction (CVPR 2019 · 198 citations)
- 2020 · MAGSAC++, a Fast, Reliable and Accurate Robust Estimator (CVPR 2020 · 337 citations)
- 2021 · Equilibrium and non-Equilibrium regimes in the learning of Restricted Boltzmann Machines (NeurIPS 2021 · 36 citations)
- 2022 · RecDis-SNN: Rectifying Membrane Potential Distribution for Directly Training Spiking Neural Networks (CVPR 2022 · 85 citations)
- 2023 · Explaining the effects of non-convergent MCMC in the training of Energy-Based Models (ICML 2023 · 5 citations)
- 2024 · A Computational Framework for Solving Wasserstein Lagrangian Flows (ICML 2024 · 4 citations)
- 2025 · Sampling Binary Data by Denoising through Score Functions (ICML 2025 · 2 citations)
- 2026 · “Do Diffusion Models Dream of Electric Planes?” Discrete and Continuous Simulation-Based Inference for Aircraft Design (ICML 2026 · 0 citations)
Earliest papers here
- Deep Structured Energy Based Models for Anomaly Detection (ICML 2016 · 249 citations)
- Partition Functions from Rao-Blackwellized Tempered Sampling (ICML 2016 · 9 citations)
- Pliable Rejection Sampling (ICML 2016)
Benchmark records
The best number each year that beat every earlier one, among papers of this approach reporting their own method. Numbers are extracted by AI from each paper's text; check the paper before citing.
CIFAR-10 · FID (lower is better)
7 papers, 2019–2025 · one report since 2024, not better
| Year | Best so far | Set by |
|---|---|---|
| 2019 | 44.5 | Learning Non-Convergent Non-Persistent Short-Run MCMC Toward Energy-Based Model (NeurIPS 2019 · 96 citations) |
| 2021 | 30.5 | No MCMC for me: Amortized sampling for fast and stable training of energy-based models (ICLR 2021 · 7 citations) |
CelebA · FID (lower is better)
6 papers, 2019–2025 · one report since 2024, not better
| Year | Best so far | Set by |
|---|---|---|
| 2019 | 23.02 | Learning Non-Convergent Non-Persistent Short-Run MCMC Toward Energy-Based Model (NeurIPS 2019 · 96 citations) |
| 2020 | 9.7 | Learning Manifold Implicitly via Explicit Heat-Kernel Learning (NeurIPS 2020 · 2 citations) |
| 2021 | 4 | Exploiting Chain Rule and Bayes' Theorem to Compare Probability Distributions (NeurIPS 2021 · 1 citation) |
What has been tried
100 papers here report 1,000 measured changes (a component added, removed or swapped, compared with a baseline): helped 68%, no clear effect 9%, hurt 18%, mixed 5%. Papers mostly publish changes that helped, so "helped" is over-represented.
Ablations in recent papers
| What was changed | Measured on | Result | Effect | Paper |
|---|---|---|---|---|
| Increase the number of Bernoulli measurements | Synthetic binary mixtures · Wasserstein distance to the clean distribution | Helped | Sampling Binary Data by Denoising through Score Functions (ICML 2025 · 2 citations) | |
| Train amortized warm-starts with reverse KL instead of no warm-start | CIFAR-10, SVHN, CelebA · FID | Helped | Sample as you Infer: Predictive Coding with Langevin Dynamics (ICML 2024 · 2 citations) | |
| Use fourth-order Adams-Bashforth instead of forward Euler | Two-dimensional Bayesian posteriors · KSD | Helped | Sampling in Unit Time with Kernel Fisher-Rao Flow (ICML 2024 · 2 citations) | |
| use small initial eigenvalues rather than initial values above the fixed point | Synthetic finite-sample data · coupling reconstruction error | Mixed | A Theoretical Framework For Overfitting In Energy-based Modeling (ICML 2025 · 1 citation) | |
| Increase latent standard deviation from σ=20 to σ=30 for learned interpolation | Gaussian Mixture Model (40 modes) · ESS | 0.605 -> 0.922 | Helped | Neural Sampling from Boltzmann Densities: Fisher-Rao Curves in the Wasserstein Geometry (ICLR 2025 · 1 citation) |
| Add reverse-SDE sampler samples to the buffer (iDEM rather than prior-only pDEM) | DW-4 · sample energy distribution | Helped | Iterated Denoising Energy Matching for Sampling from Boltzmann Densities (ICML 2024 · 1 citation) | |
| Initialize the test-time Gibbs sampler at data rather than noise | Image generation · sample quality | Helped | Exponential-Family Harmoniums with Neural Sufficient Statistics (AAAI 2025 · 0 citations) | |
| Increase polynomial order from r=1 to r=2 | RBM, perturbation 0.02 · null rejection rate | 0.51 -> 1.00 | Helped | The Polynomial Stein Discrepancy for Assessing Moment Convergence (ICML 2025 · 0 citations) |
| Use CTSM-v instead of TSM | MNIST · Trainability | Helped | Density Ratio Estimation with Conditional Probability Paths (ICML 2025 · 0 citations) | |
| Add one resampling step to NETS-PINN | 40-mode GMM (d=2) · ESS | 0.979 ± 0.002 -> 0.993 ± 0.004 | Helped | NETS: A Non-equilibrium Transport Sampler (ICML 2025 · 0 citations) |
| Increase stochasticity from α=0.005 to α=0.01 | CelebA 128×128 male→female · FID | 10.60 -> 14.68 | Hurt | Categorical Schrödinger Bridge Matching (ICML 2025 · 0 citations) |
| Use a linear rather than constant flip-schedule | Binarized MNIST · FID | Helped | Discrete Markov Probabilistic Models: An Improved Discrete Score-Based Framework with sharp convergence bounds under minimal assumptions (ICML 2025 · 0 citations) |
Baseline numbers that disagree
The same baseline on the same benchmark and metric, reported more than 5% apart by different papers here. Training budgets, data splits and reimplementations differ, so state which number you compare with.
| Baseline | Benchmark | Metric | Reported | Papers |
|---|---|---|---|---|
| DCGAN | CelebA | FID | 12.5 – 52.5 | 3 papers, e.g. AAAI 2025 and NeurIPS 2021 |
| VAE | CelebA | FID | 38.76 – 79.09 | 3 papers, e.g. AAAI 2025 and NeurIPS 2019 |
| VAE | MNIST | FID | 16.14 – 32.86 | 2 papers, e.g. ICML 2023 and ICLR 2022 |
| DCGAN | CIFAR-10 | FID | 30.2 – 37.11 | 2 papers, e.g. NeurIPS 2021 and ICML 2023 |
| DCGAN | LSUN Bedroom | FID | 54.17 – 61.7 | 2 papers, e.g. NeurIPS 2019 and NeurIPS 2021 |
What reviewers will expect
Datasets and baselines named in the 38 papers of this approach from 2025–2026 that have a full-text summary. Leaving out the common ones is a frequent review question.
Datasets
- MNIST · 8 of 38 papers
- CIFAR-10 · 5 of 38 papers
- CelebA · 2 of 38 papers
- CelebA-HQ · 2 of 38 papers
- synthetic Gaussian samples · 2 of 38 papers
Baselines
- Glow · 2 of 38 papers
- TSM · 2 of 38 papers
- linear interpolation · 2 of 38 papers
- MBAR · 2 of 38 papers
Recent preprints
Loading recent arXiv preprints…
Who publishes on it
Institutions on the most papers of this approach since 2023 (of 82 papers; from OpenAlex and the papers' affiliations).
- University of Texas, Austin · 5 papers
- Georgia Institute of Technology · 4 papers
- Massachusetts Institute of Technology · 4 papers
- Purdue University · 3 papers
- Google · 3 papers
- University College London · 3 papers
- Imperial College London · 3 papers
- Microsoft · 3 papers
- Université de Montréal · 3 papers
- University of Cambridge · 3 papers
Use it
Download BibTeX of 40 key papersOpen the topic in the interactive map
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Related approaches
Same keyword cluster
- Score-based generative modeling analysis (128 papers)
- Flow matching and flow sampling (144 papers)
Elsewhere in the topic
- Likelihood-free and graphical model estimation (161 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)
- Tractable probabilistic models (90 papers)
- Variational inference theory and gradients (89 papers)
- Hamiltonian Monte Carlo (89 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).