Research map / Probabilistic and scientific modeling / Variational and generative sampling
Flow matching and flow sampling
Learns straighter flows and samples from unnormalized densities via flow matching.
144 accepted papers at ICML, NeurIPS, ICLR, CVPR and AAAI (2019–2026) · an approach in Variational and generative sampling, keyword cluster “diffusion · score · matching”
State History Benchmarks Tried Baselines Checklist Preprints Who Export
Where it stands
Leveling off Several papers from 2025–26 still report on 1 tracked benchmark, but the best result has barely moved since 2024.
25 papers in 2023–24 and 113 in 2025–26 (at ICML, NeurIPS, ICLR, CVPR and AAAI); its share of the topic grew, from 6.0% to 22.6%.
Open questions the data points to
- Papers report DDPM on CIFAR-10 (FID) anywhere from 3.17 to 7.48: comparisons against it depend on whose number you take.
What looks settled
- CIFAR-10 (FID): best up to 2024 2.35, best in 2025–26 2.36 from 6 papers, at most 0.2% better, if at all.
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
- 2019 · Sliced-Wasserstein Flows: Nonparametric Generative Modeling via Optimal Transport and Diffusions (ICML 2019 · 6 citations)
- 2020 · ACFlow: Flow Models for Arbitrary Conditional Likelihoods (ICML 2020 · 15 citations)
- 2022 · Poisson Flow Generative Models (NeurIPS 2022 · 11 citations)
- 2023 · Flow Matching for Generative Modeling (ICLR 2023 · 108 citations)
- 2024 · Discrete Flow Matching (NeurIPS 2024 · 16 citations)
- 2025 · TensoFlow: Tensorial Flow-based Sampler for Inverse Rendering (CVPR 2025 · 3 citations)
- 2026 · AlphaFlow: Understanding and Improving MeanFlow Models (ICLR 2026 · 1 citation)
Earliest papers here
- Sliced-Wasserstein Flows: Nonparametric Generative Modeling via Optimal Transport and Diffusions (ICML 2019 · 6 citations)
- ACFlow: Flow Models for Arbitrary Conditional Likelihoods (ICML 2020 · 15 citations)
- Poisson Flow Generative Models (NeurIPS 2022 · 11 citations)
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)
11 papers, 2022–2025 · flat since 2024
| Year | Best so far | Set by |
|---|---|---|
| 2022 | 2.35 | Poisson Flow Generative Models (NeurIPS 2022 · 11 citations) |
What has been tried
57 papers here report 543 measured changes (a component added, removed or swapped, compared with a baseline): helped 71%, no clear effect 5%, hurt 21%, mixed 3%. Papers mostly publish changes that helped, so "helped" is over-represented.
Ablations in recent papers
| What was changed | Measured on | Result | Effect | Paper |
|---|---|---|---|---|
| use conditional coupling instead of unconditional coupling | Conditional text generation · Llama-3 generative perplexity | 10.3 -> 9.7 | Helped | Discrete Flow Matching (NeurIPS 2024 · 16 citations) |
| Replace ICNN with MLP | Wasserstein-2 benchmark · convergence | Hurt | Optimal Flow Matching: Learning Straight Trajectories in Just One Step (NeurIPS 2024 · 11 citations) | |
| add optimal transport | Binarized MNIST · FID | 5.15 -> 4.62 | Helped | Categorical Flow Matching on Statistical Manifolds (NeurIPS 2024 · 5 citations) |
| Reduce model size | Molecular generation · Valid-and-unique score | Helped | Variational Flow Matching for Graph Generation (NeurIPS 2024 · 4 citations) | |
| add a learnable diffuse sampler rather than use a pre-defined diffuse sampler | TensoSDF synthetic (Average) · PSNR | 26.433 -> 26.933 | Helped | TensoFlow: Tensorial Flow-based Sampler for Inverse Rendering (CVPR 2025 · 3 citations) |
| Add repulsion interaction energy | AAV medium · Diversity | 5.86 -> 6.22 | Helped | Energy Matching: Unifying Flow Matching and Energy-Based Models for Generative Modeling (NeurIPS 2025 · 1 citation) |
| add noise to interpolants (σ=0.05) | Gaussian mixture d=3 Gen · MMD | 0.0034 -> 0.0018 | Helped | Gradient Variance Reveals Failure Modes in Flow-Based Generative Models (NeurIPS 2025 · 1 citation) |
| replace exact particle interaction with approximate sampling | CIFAR-10 · FID | 8.31 -> 24.86 | Hurt | Deep MMD Gradient Flow without adversarial training (ICLR 2025 · 1 citation) |
| Reflow (2-RF) versus one-step Rectified Flow (1-RF) | seeds, path geometry · discrete kinetic action | 3179.2 to 3006.9 (lower) | Helped | From Baselines to Transport Geodesics: Axiomatic Attribution via Optimal Generative Flows (NeurIPS 2026 · 0 citations) |
| Add embedding and augmentation to MMDSW dataset distillation | MNIST and Fashion-MNIST, p=10 · classifier accuracy | MNIST: 96.4 ± 0.2 -> 96.4 ± 0.3; FMNIST: 78.0 ± 0.9 -> 78.9 ± 1.2 | Hurt | Flowing Datasets with Wasserstein over Wasserstein Gradient Flows (ICML 2025 · 0 citations) |
| Increase KL loss weight from 2e-3 to 5e-3 | CIFAR-10, higher function evaluations · FID | 4.430 -> 4.349 (100 NFE); 3.642 -> 3.582 (1000 NFE) | Helped | Variational Rectified Flow Matching (ICML 2025 · 0 citations) |
| Use ΔF-scale losses without state flow regularization | Permutation n=20 · C(k) L1 | 0.017 ± 0.002 -> 0.453 ± 0.002 | Hurt | Revisiting Non-Acyclic GFlowNets in Discrete Environments (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 |
|---|---|---|---|---|
| DDPM | CIFAR-10 | FID | 3.17 – 7.48 | 3 papers, e.g. ICLR 2025 and ICLR 2023 |
What reviewers will expect
Datasets and baselines named in the 70 papers of this approach from 2025–2026 that have a full-text summary. Leaving out the common ones is a frequent review question.
Datasets
- CIFAR-10 · 17 of 70 papers
- MNIST · 13 of 70 papers
- CelebA · 5 of 70 papers
- ImageNet · 4 of 70 papers
- QM9 · 4 of 70 papers
- Fashion-MNIST · 3 of 70 papers
- ImageNet-32 · 3 of 70 papers
- LSUN Church · 2 of 70 papers
Baselines
- rectified flow · 5 of 70 papers
- OT-CFM · 5 of 70 papers
- DDPM · 5 of 70 papers
- EDM · 4 of 70 papers
- Flow Matching · 3 of 70 papers
- SEDD · 3 of 70 papers
- FM · 3 of 70 papers
- Dirichlet FM · 2 of 70 papers
Recent preprints
Loading recent arXiv preprints…
Who publishes on it
Institutions on the most papers of this approach since 2023 (of 138 papers; from OpenAlex and the papers' affiliations).
- University of Montreal · 5 papers
- Mila · 4 papers
- Meta · 4 papers
- Université de Montréal · 4 papers
- University of Illinois, Urbana Champaign · 4 papers
- Google DeepMind · 4 papers
- Purdue University · 4 papers
- McGill University · 3 papers
- New York University · 3 papers
- Seoul National University · 3 papers
Use it
Download BibTeX of 29 key papersOpen the topic in the interactive map
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Related approaches
Same keyword cluster
- Posterior sampling with diffusion guidance (137 papers)
- Score-based generative modeling analysis (128 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).