Research map / Probabilistic and scientific modeling / Variational and generative sampling
Expressive invertible architectures
Improves flow expressiveness via variational dequantization and residual or Koopman-based designs.
76 accepted papers at ICML, NeurIPS, ICLR, CVPR and AAAI (2017–2026) · an approach in Variational and generative sampling, keyword cluster “flows · normalizing · invertible”
State History Benchmarks Tried Checklist Preprints Who Export
Where it stands
Few recent reports None of the tracked benchmarks has a report from 2025–26.
8 papers in 2023–24 and 25 in 2025–26 (at ICML, NeurIPS, ICLR, CVPR and AAAI); its share of the topic grew, from 1.9% to 5.0%.
No longer reported by papers here: CIFAR10 (bits/dim, last in 2022); CIFAR-10 (FID, last in 2022).
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
- 2017 · Maximum Entropy Flow Networks (ICLR 2017 · 7 citations)
- 2018 · Glow: Generative Flow with Invertible 1x1 Convolutions (NeurIPS 2018 · 177 citations)
- 2019 · Flow++: Improving Flow-Based Generative Models with Variational Dequantization and Architecture Design (ICML 2019 · 206 citations)
- 2020 · Approximation Capabilities of Neural ODEs and Invertible Residual Networks (ICML 2020 · 25 citations)
- 2021 · iVPF: Numerical Invertible Volume Preserving Flow for Efficient Lossless Compression (CVPR 2021 · 40 citations)
- 2022 · Manifold Interpolating Optimal-Transport Flows for Trajectory Inference (NeurIPS 2022 · 25 citations)
- 2023 · SE(3) Equivariant Augmented Coupling Flows (NeurIPS 2023 · 3 citations)
- 2024 · Flow Matching on General Geometries (ICLR 2024 · 5 citations)
- 2025 · Scalable Equilibrium Sampling with Sequential Boltzmann Generators (ICML 2025 · 1 citation)
- 2026 · Autoregressive Boltzmann Generators (ICML 2026 · 0 citations)
Earliest papers here
- Maximum Entropy Flow Networks (ICLR 2017 · 7 citations)
- Glow: Generative Flow with Invertible 1x1 Convolutions (NeurIPS 2018 · 177 citations)
- Variational Probability Flow for Biologically Plausible Training of Deep Neural Networks (AAAI 2018 · 4 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.
CIFAR10 · bits/dim (lower is better)
5 papers, 2019–2022 · not reported since 2022
| Year | Best so far | Set by |
|---|---|---|
| 2019 | 3.08 | Flow++: Improving Flow-Based Generative Models with Variational Dequantization and Architecture Design (ICML 2019 · 206 citations) |
CIFAR-10 · FID (lower is better)
4 papers, 2019–2022 · not reported since 2022
| Year | Best so far | Set by |
|---|---|---|
| 2019 | 46.37 | Residual Flows for Invertible Generative Modeling (NeurIPS 2019 · 175 citations) |
| 2022 | 15.8 | A Tale of Two Flows: Cooperative Learning of Langevin Flow and Normalizing Flow Toward Energy-Based Model (ICLR 2022 · 8 citations) |
What has been tried
59 papers here report 578 measured changes (a component added, removed or swapped, compared with a baseline): helped 69%, no clear effect 8%, hurt 17%, 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 |
|---|---|---|---|---|
| replace biharmonic distance with diffusion distance | Stanford Bunny and Spot the Cow meshes · test NLL | Stanford Bunny k=10: 1.06 ±0.05 -> 1.16 ±0.02; k=50: 1.55 ±0.01 -> 1.48 ±0.01; k=100: 1.49 ±0.01 -> 1.53 ±0.01; Spot the | Mixed | Flow Matching on General Geometries (ICLR 2024 · 5 citations) |
| Add center-of-mass adjusted proposal energy | Trialanine · \(\mathbb{T}\text{‑}\mathcal{W}_2\) | Helped | Scalable Equilibrium Sampling with Sequential Boltzmann Generators (ICML 2025 · 1 citation) | |
| add regularization R to the unstable FM loss | 2D checkerboard RL task · training stability | Helped | Ergodic Generative Flows (ICML 2025 · 0 citations) | |
| Add a residual connection for the conditioning input | Numerical experiments · performance | Helped | Computing Optimal Transport Maps and Wasserstein Barycenters Using Conditional Normalizing Flows (ICML 2025 · 0 citations) | |
| add the Metropolis-Hastings correction to the HMC flow | Banana, Funnel, Cross, and Warped Gaussian · TV distance | Helped | Asymptotically exact variational flows via involutive MCMC kernels (NeurIPS 2025 · 0 citations) | |
| Use sampling steps (2,50) rather than (1,100) | 2D N→6N · 2-SWD | 0.070 -> 0.037 | Helped | Towards Hierarchical Rectified Flow (ICLR 2025 · 0 citations) |
| Add calibration by optimizing c* rather than fixing c | UAV · ELBO (nats/dim) | 6.95 (± 1.2) vs 7.86 (± 1.0) | Hurt | Rare event modeling with self-regularized normalizing flows: what can we learn from a single failure? (ICLR 2025) |
What reviewers will expect
Datasets and baselines named in the 16 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 · 4 of 16 papers
- CIFAR-10 · 3 of 16 papers
Baselines
- Flow Matching · 2 of 16 papers
- Detailed Balance · 2 of 16 papers
- Trajectory Balance · 2 of 16 papers
Recent preprints
Loading recent arXiv preprints…
Who publishes on it
Institutions on the most papers of this approach since 2023 (of 33 papers; from OpenAlex and the papers' affiliations).
- University of British Columbia · 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
- Normalizing flow training and design (88 papers)
- Flow-based density estimation (29 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).