mlsanityData to 7 Oct 2026

Multisample Flow Matching: Straightening Flows with Minibatch Couplings

arXiv 2304.14772 ↗First posted 28 Apr 2023cs.LGcited by 267

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

Abstract (arXiv)

Simulation-free methods for training continuous-time generative models construct probability paths that go between noise distributions and individual data samples. Recent works, such as Flow Matching, derived paths that are optimal for each data sample. However, these algorithms rely on independent data and noise samples, and do not exploit underlying structure in the data distribution for constructing probability paths. We propose Multisample Flow Matching, a more general framework that uses non-trivial couplings between data and noise samples while satisfying the correct marginal constraints. At very small overhead costs, this generalization allows us to (i) reduce gradient variance during training, (ii) obtain straighter flows for the learned vector field, which allows us to generate high-quality samples using fewer function evaluations, and (iii) obtain transport maps with lower cost in high dimensions, which has applications beyond generative modeling. Importantly, we do so in a completely simulation-free manner with a simple minimization objective. We show that our proposed methods improve sample consistency on downsampled ImageNet data sets, and lead to better low-cost sample generation.

Key facts. Cited by 267 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 42 of its 79 references that are in the map. First posted on arXiv 28 Apr 2023.

Builds on

42 of 79 references.

Closest ancestors · 4

Same direction, newest first

  1. 2023Flow Matching on General Geometries7 Feb
  2. 2022Flow Matching for Generative Modeling6 Oct
  3. 2022Rectified Flow: A Marginal Preserving Approach to Optimal Transport29 Sep
  4. 2022Flow Straight and Fast: Learning to Generate and Transfer Data with Rectified Flow7 Sep

Other references · 38

  1. 2020Denoising Diffusion Probabilistic Modelscited by 20,851
  2. 2019PyTorch: An Imperative Style, High-Performance Deep Learning Librarycited by 20,160
  3. 2020Score-Based Generative Modeling through Stochastic Differential Equationscited by 8,964
  4. 2021Diffusion Models Beat GANs on Image Synthesiscited by 8,185
  5. 2022Hierarchical Text-Conditional Image Generation with CLIP Latentscited by 6,539
  6. 2022Photorealistic Text-to-Image Diffusion Models with Deep Language Understandingcited by 6,322
  7. 2018Neural Ordinary Differential Equationscited by 3,733
  8. 2016Perceptual Losses for Real-Time Style Transfer and Super-Resolutioncited by 2,678
  9. 2013Sinkhorn Distances: Lightspeed Computation of Optimal Transportation Distancescited by 2,277
  10. 2016Density estimation using Real NVPcited by 2,029
  11. 2022Building Normalizing Flows with Stochastic Interpolantscited by 964
  12. 2018Computational Optimal Transportcited by 765
26 more
  1. 2021Maximum Likelihood Training of Score-Based Diffusion Modelscited by 670
  2. 2022Make-A-Scene: Scene-Based Text-to-Image Generation with Human Priorscited by 487
  3. 2015A Neural Algorithm of Artistic Stylecited by 480
  4. 2017A Downsampled Variant of ImageNet as an Alternative to the CIFAR datasetscited by 374
  5. 2017Learning Generative Models with Sinkhorn Divergencescited by 310
  6. 2017MMD GAN: Towards Deeper Understanding of Moment Matching Networkcited by 251
  7. 2020How to train your neural ODE: the world of Jacobian and kinetic regularizationcited by 228
  8. 2017Near-linear time approximation algorithms for optimal transport via Sinkhorn iterationcited by 219
  9. 2019Optimal transport mapping via input convex neural networkscited by 202
  10. 2020TrajectoryNet: A Dynamic Optimal Transport Network for Modeling Cellular Dynamicscited by 155
  11. 2020OT-Flow: Fast and Accurate Continuous Normalizing Flows via Optimal Transportcited by 143
  12. 2017Large-Scale Optimal Transport and Mapping Estimationcited by 120
  13. 2020Convex Potential Flows: Universal Probability Distributions with Optimal Transport and Convex Optimizationcited by 89
  14. 2021Entropic estimation of optimal transport mapscited by 87
  15. 2023Minimizing Trajectory Curvature of ODE-based Generative Modelscited by 87
  16. 2019Learning with minibatch Wasserstein : asymptotic and gradient propertiescited by 83
  17. 2021Minibatch optimal transport distances; analysis and applicationscited by 62
  18. 2022Supervised Training of Conditional Monge Mapscited by 60
  19. 2013Regularized Discrete Optimal Transportcited by 54
  20. 2021Improving Mini-batch Optimal Transport via Partial Transportationcited by 40
  21. 2017Optimal Transport for Diffeomorphic Registrationcited by 39
  22. 2022Neural Optimal Transport with General Cost Functionalscited by 34
  23. 2022On amortizing convex conjugates for optimal transportcited by 30
  24. 2020Learning normalizing flows from Entropy-Kantorovich potentialscited by 18
  25. 2022Neural Unbalanced Optimal Transport via Cycle-Consistent Semi-Couplingscited by 16
  26. 2019No-collision Transportation Mapscited by 5

Built on by

Cited by year (2026 to 7 Oct)

Citing papers per year: 2023: 17; 2024: 70; 2025: 93; 2026: 87.

267 papers.

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By area:

  1. 2024SiT: Exploring Flow and Diffusion-based Generative Models with Scalable Interpolant Transformerscited by 707
  2. 2024Discrete Flow Matchingcited by 301
  3. 2023Denoising Diffusion Bridge Modelscited by 171
  4. 2023Flow Matching in Latent Spacecited by 155
  5. 2023SE(3)-Stochastic Flow Matching for Protein Backbone Generationcited by 147
  6. 2023Equivariant flow matchingcited by 131
  7. 2024Dirichlet Flow Matching with Applications to DNA Sequence Designcited by 110
  8. 2024Improving the Training of Rectified Flowscited by 106
  9. 2024AlphaFold Meets Flow Matching for Generating Protein Ensemblescited by 105
  10. 2024Consistency Flow Matching: Defining Straight Flows with Velocity Consistencycited by 101
  11. 2023Guided Flows for Generative Modeling and Decision Makingcited by 99
  12. 2024Flow map matching with stochastic interpolants: A mathematical framework for consistency modelscited by 99
38 more
  1. 2023Unpaired Image-to-Image Translation via Neural Schr"odinger Bridgecited by 96
  2. 2024PeRFlow: Piecewise Rectified Flow as Universal Plug-and-Play Acceleratorcited 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. 2024Normalizing Flows are Capable Generative Modelscited by 89
  6. 2023Simulation-free Schr"odinger bridges via score and flow matchingcited by 81
  7. 2024Optimal Flow Matching: Learning Straight Trajectories in Just One Stepcited by 74
  8. 2025Proteina: Scaling Flow-based Protein Structure Generative Modelscited by 63
  9. 2023Equivariant Flow Matching with Hybrid Probability Transportcited by 59
  10. 2024Rectified Diffusion: Straightness Is Not Your Need in Rectified Flowcited by 59
  11. 2025On the Closed-Form of Flow Matching: Generalization Does Not Arise from Target Stochasticitycited by 48
  12. 2023A Computational Framework for Solving Wasserstein Lagrangian Flowscited by 43
  13. 2024Neural Flow Diffusion Models: Learnable Forward Process for Improved Diffusion Modellingcited by 43
  14. 2024Meta Flow Matching: Integrating Vector Fields on the Wasserstein Manifoldcited by 41
  15. 2024ET-Flow: Equivariant Flow-Matching for Molecular Conformer Generationcited by 41
  16. 2024Imagine Flash: Accelerating Emu Diffusion Models with Backward Distillationcited by 37
  17. 2024Sequence-Augmented SE(3)-Flow Matching For Conditional Protein Backbone Generationcited by 36
  18. 2024Conditional Wasserstein Distances with Applications in Bayesian OT Flow Matchingcited by 34
  19. 2024Simple ReFlow: Improved Techniques for Fast Flow Modelscited by 34
  20. 2024Unveil Inversion and Invariance in Flow Transformer for Versatile Image Editingcited by 34
  21. 2023Unbalancedness in Neural Monge Maps Improves Unpaired Domain Translationcited by 32
  22. 2025FlowTok: Flowing Seamlessly Across Text and Image Tokenscited by 31
  23. 2023Harmonic Self-Conditioned Flow Matching for Multi-Ligand Docking and Binding Site Designcited by 29
  24. 2023Adaptive Guidance: Training-free Acceleration of Conditional Diffusion Modelscited by 29
  25. 2024Video Diffusion Models: A Surveycited by 28
  26. 2023GENOT: Entropic (Gromov) Wasserstein Flow Matching with Applications to Single-Cell Genomicscited by 27
  27. 2024Wasserstein Flow Matching: Generative modeling over families of distributionscited by 27
  28. 2023Generative Modeling with Phase Stochastic Bridgescited by 24
  29. 2024Dynamic Conditional Optimal Transport through Simulation-Free Flowscited by 24
  30. 2023Augmented Bridge Matchingcited by 21
  31. 2024Trajectory Flow Matching with Applications to Clinical Time Series Modelingcited by 21
  32. 2025Temporal Difference Flowscited by 20
  33. 2025Joint Velocity-Growth Flow Matching for Single-Cell Dynamics Modelingcited by 20
  34. 2025Towards Hierarchical Rectified Flowcited by 19
  35. 2025One-Step Flow Policy Mirror Descentcited by 18
  36. 2023Gaussian Interpolation Flowscited by 17
  37. 2024ParetoFlow: Guided Flows in Multi-Objective Optimizationcited by 17
  38. 2025Not-So-Optimal Transport Flows for 3D Point Cloud Generationcited by 17

50 most cited of 267 All 267 (JSON)

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  1. 2026ODE-free Neural Flow Matching for One-Step Generative Modeling
  2. 2025Carr'e du champ flow matching: better quality-generalisation tradeoff in generative models
  3. 2026Temporal Pair Consistency for Variance-Reduced Flow Matching
  4. 2025Blockwise Flow Matching: Improving Flow Matching Models For Efficient High-Quality Generation
  5. 2025Generative Modeling with Continuous Flows: Sample Complexity of Flow Matching
  6. 2026Difficulty-Calibrated Interpolation Paths for Conditional Flow Matching
  7. 2023Straighter Flow Matching via a Diffusion-Based Coupling Prior
  8. 2026Training Flow Matching: The Role of Weighting and Parameterization