mlsanityData to 7 Oct 2026

Improving and generalizing flow-based generative models with minibatch optimal transport

arXiv 2302.00482 ↗First posted 1 Feb 2023cs.LGcited by 835

On the map: Diffusion models → Flow matching, time series and science

Abstract (arXiv)

Continuous normalizing flows (CNFs) are an attractive generative modeling technique, but they have been held back by limitations in their simulation-based maximum likelihood training. We introduce the generalized conditional flow matching (CFM) technique, a family of simulation-free training objectives for CNFs. CFM features a stable regression objective like that used to train the stochastic flow in diffusion models but enjoys the efficient inference of deterministic flow models. In contrast to both diffusion models and prior CNF training algorithms, CFM does not require the source distribution to be Gaussian or require evaluation of its density. A variant of our objective is optimal transport CFM (OT-CFM), which creates simpler flows that are more stable to train and lead to faster inference, as evaluated in our experiments. Furthermore, we show that when the true OT plan is available, our OT-CFM method approximates dynamic OT. Training CNFs with CFM improves results on a variety of conditional and unconditional generation tasks, such as inferring single cell dynamics, unsupervised image translation, and Schr"odinger bridge inference.

Key facts. Cited by 835 papers in the map (data through 7 Oct 2026). Placed in Flow matching, time series and science, one of 14 directions in Diffusion models. Builds on 57 of its 91 references that are in the map. First posted on arXiv 1 Feb 2023.

Builds on

57 of 91 references.

Closest ancestors · 3

Same direction, newest first

  1. 2022Flow Matching for Generative Modeling6 Oct
  2. 2022Rectified Flow: A Marginal Preserving Approach to Optimal Transport29 Sep
  3. 2022Flow Straight and Fast: Learning to Generate and Transfer Data with Rectified Flow7 Sep

Other references · 54

  1. 2020Denoising Diffusion Probabilistic Modelscited by 20,851
  2. 2019PyTorch: An Imperative Style, High-Performance Deep Learning Librarycited by 20,160
  3. 2020Denoising Diffusion Implicit Modelscited by 9,655
  4. 2020Score-Based Generative Modeling through Stochastic Differential Equationscited by 8,964
  5. 2021Diffusion Models Beat GANs on Image Synthesiscited by 8,185
  6. 2015Deep Unsupervised Learning using Nonequilibrium Thermodynamicscited by 7,005
  7. 2019Generative Modeling by Estimating Gradients of the Data Distributioncited by 4,067
  8. 2021Improved Denoising Diffusion Probabilistic Modelscited by 3,736
  9. 2018Neural Ordinary Differential Equationscited by 3,733
  10. 2014Deep Learning Face Attributes in the Wildcited by 3,679
  11. 2013Sinkhorn Distances: Lightspeed Computation of Optimal Transportation Distancescited by 2,277
  12. 2015Variational Inference with Normalizing Flowscited by 2,161
38 more
  1. 2022DPM-Solver: A Fast ODE Solver for Diffusion Probabilistic Model Sampling in Around 10 Stepscited by 1,961
  2. 2021Structured Denoising Diffusion Models in Discrete State-Spacescited by 1,665
  3. 2020Improved Techniques for Training Score-Based Generative Modelscited by 1,036
  4. 2022Building Normalizing Flows with Stochastic Interpolantscited by 964
  5. 2018Computational Optimal Transportcited by 765
  6. 2021Diffusion Schr"odinger Bridge with Applications to Score-Based Generative Modelingcited by 594
  7. 2017Self-Normalizing Neural Networkscited by 591
  8. 2018FFJORD: Free-form Continuous Dynamics for Scalable Reversible Generative Modelscited by 584
  9. 2022Analytic-DPM: an Analytic Estimate of the Optimal Reverse Variance in Diffusion Probabilistic Modelscited by 331
  10. 2017Learning Generative Models with Sinkhorn Divergencescited by 310
  11. 2022DiffDock: Diffusion Steps, Twists, and Turns for Molecular Dockingcited by 307
  12. 2013A survey of the Schr"odinger problem and some of its connections with optimal transportcited by 286
  13. 2020Scalable Gradients for Stochastic Differential Equationscited by 264
  14. 2020How to train your neural ODE: the world of Jacobian and kinetic regularizationcited by 228
  15. 2021Likelihood Training of Schr"odinger Bridge using Forward-Backward SDEs Theorycited by 216
  16. 2018DeepJDOT: Deep Joint Distribution Optimal Transport for Unsupervised Domain Adaptationcited by 212
  17. 2019Optimal transport mapping via input convex neural networkscited by 202
  18. 2022Learning Fast Samplers for Diffusion Models by Differentiating Through Sample Qualitycited by 181
  19. 2021Path Integral Sampler: a stochastic control approach for samplingcited by 175
  20. 2014Deep Learning Face Representation by Joint Identification-Verificationcited by 162
  21. 2020TrajectoryNet: A Dynamic Optimal Transport Network for Modeling Cellular Dynamicscited by 155
  22. 2020OT-Flow: Fast and Accurate Continuous Normalizing Flows via Optimal Transportcited by 143
  23. 2021Solving Schr"odinger Bridges via Maximum Likelihoodcited by 140
  24. 2021Unbalanced minibatch Optimal Transport; applications to Domain Adaptationcited by 123
  25. 2022Neural Optimal Transportcited by 123
  26. 2021Deep Generative Learning via Schr"odinger Bridgecited by 103
  27. 2022Let us Build Bridges: Understanding and Extending Diffusion Generative Modelscited by 102
  28. 2021Do Neural Optimal Transport Solvers Work? A Continuous Wasserstein-2 Benchmarkcited by 95
  29. 2022Action Matching: Learning Stochastic Dynamics from Samplescited by 94
  30. 2021Proximal Optimal Transport Modeling of Population Dynamicscited by 91
  31. 2019Learning with minibatch Wasserstein : asymptotic and gradient propertiescited by 83
  32. 2021Moser Flow: Divergence-based Generative Modeling on Manifoldscited by 67
  33. 2022Manifold Interpolating Optimal-Transport Flows for Trajectory Inferencecited by 63
  34. 2021Minibatch optimal transport distances; analysis and applicationscited by 62
  35. 2022Conditional Simulation Using Diffusion Schr"odinger Bridgescited by 58
  36. 2022Matching Normalizing Flows and Probability Paths on Manifoldscited by 57
  37. 2022Deep Generalized Schr"odinger Bridgecited by 47
  38. 2020Entropy-Regularized 2-Wasserstein Distance between Gaussian Measurescited by 32

50 most cited of 54 All 54 (JSON)

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Cited by year (2026 to 7 Oct)

Citing papers per year: 2023: 25; 2024: 129; 2025: 338; 2026: 343.

835 papers.

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  1. 2024SiT: Exploring Flow and Diffusion-based Generative Models with Scalable Interpolant Transformerscited by 707
  2. 2024Discrete Flow Matchingcited by 301
  3. 2026Causal World Modeling for Robot Controlcited by 289
  4. 2024Simplifying, Stabilizing and Scaling Continuous-Time Consistency Modelscited by 276
  5. 2023Denoising Diffusion Bridge Modelscited by 171
  6. 2025Sundial: A Family of Highly Capable Time Series Foundation Modelscited by 168
  7. 2023SE(3)-Stochastic Flow Matching for Protein Backbone Generationcited by 147
  8. 2024MMAudio: Taming Multimodal Joint Training for High-Quality Video-to-Audio Synthesiscited by 134
  9. 2024Iterated Denoising Energy Matching for Sampling from Boltzmann Densitiescited by 113
  10. 2024Dirichlet Flow Matching with Applications to DNA Sequence Designcited by 110
  11. 2024Consistency Flow Matching: Defining Straight Flows with Velocity Consistencycited by 101
  12. 2024Flow map matching with stochastic interpolants: A mathematical framework for consistency modelscited by 99
38 more
  1. 2023On the Stability of Iterative Retraining of Generative Models on their own Datacited by 98
  2. 2025Representation Entanglement for Generation: Training Diffusion Transformers Is Much Easier Than You Thinkcited by 95
  3. 2023Stochastic interpolants with data-dependent couplingscited by 94
  4. 2024PnP-Flow: Plug-and-Play Image Restoration with Flow Matchingcited by 92
  5. 2023Simulation-free Schr"odinger bridges via score and flow matchingcited by 81
  6. 2024DepthFM: Fast Monocular Depth Estimation with Flow Matchingcited by 76
  7. 2024Optimal Flow Matching: Learning Straight Trajectories in Just One Stepcited by 74
  8. 2024Metric Flow Matching for Smooth Interpolations on the Data Manifoldcited by 74
  9. 2024Fisher Flow Matching for Generative Modeling over Discrete Datacited by 68
  10. 2025Proteina: Scaling Flow-based Protein Structure Generative Modelscited by 63
  11. 2024Riemannian Flow Matching Policy for Robot Motion Learningcited by 61
  12. 2023Generating and Imputing Tabular Data via Diffusion and Flow-based Gradient-Boosted Treescited by 60
  13. 2024Rectified Diffusion: Straightness Is Not Your Need in Rectified Flowcited by 59
  14. 2024Mixed Continuous and Categorical Flow Matching for 3D De Novo Molecule Generationcited by 53
  15. 2024Feedback Efficient Online Fine-Tuning of Diffusion Modelscited by 52
  16. 2023VoiceFlow: Efficient Text-to-Speech with Rectified Flow Matchingcited by 49
  17. 2025On the Closed-Form of Flow Matching: Generalization Does Not Arise from Target Stochasticitycited by 48
  18. 2024Deep Generative Models through the Lens of the Manifold Hypothesis: A Survey and New Connectionscited by 47
  19. 2024Sequential Controlled Langevin Diffusionscited by 47
  20. 2023Boosting Latent Diffusion with Flow Matchingcited by 44
  21. 2025On the Guidance of Flow Matchingcited by 44
  22. 2023A Computational Framework for Solving Wasserstein Lagrangian Flowscited by 43
  23. 2024Neural Flow Diffusion Models: Learnable Forward Process for Improved Diffusion Modellingcited by 43
  24. 2024Categorical Flow Matching on Statistical Manifoldscited by 43
  25. 2024Meta Flow Matching: Integrating Vector Fields on the Wasserstein Manifoldcited by 41
  26. 2023Generalized Schr"odinger Bridge Matchingcited by 40
  27. 2024SemlaFlow -- Efficient 3D Molecular Generation with Latent Attention and Equivariant Flow Matchingcited by 40
  28. 2024Flow Matching with Gaussian Process Priors for Probabilistic Time Series Forecastingcited by 40
  29. 2025Kling-Foley: Multimodal Diffusion Transformer for High-Quality Video-to-Audio Generationcited by 38
  30. 2023SE(3) Equivariant Augmented Coupling Flowscited by 37
  31. 2024Sequence-Augmented SE(3)-Flow Matching For Conditional Protein Backbone Generationcited by 36
  32. 2025Scalable Equilibrium Sampling with Sequential Boltzmann Generatorscited by 36
  33. 2024Self-Consuming Generative Models with Curated Data Provably Optimize Human Preferencescited by 35
  34. 2024Conditional Wasserstein Distances with Applications in Bayesian OT Flow Matchingcited by 34
  35. 2024Simple ReFlow: Improved Techniques for Fast Flow Modelscited by 34
  36. 2025Flow-Based Policy for Online Reinforcement Learningcited by 33
  37. 2023Unbalancedness in Neural Monge Maps Improves Unpaired Domain Translationcited by 32
  38. 2024Posterior-Mean Rectified Flow: Towards Minimum MSE Photo-Realistic Image Restorationcited by 32

50 most cited of 835 All 835 (JSON)

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  2. 2026Improving Flow Matching by Aligning Flow Divergence
  3. 2026Optimal-Transport-Guided Functional Flow Matching for Turbulent Field Generation in Hilbert Space
  4. 2025LeDiFlow: Learned Distribution-guided Flow Matching to Accelerate Image Generation
  5. 2025Terminal Velocity Matching
  6. 2023Guided Flows for Generative Modeling and Decision Making
  7. 2023Multisample Flow Matching: Straightening Flows with Minibatch Couplings
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