mlsanityData to 7 Oct 2026

Flow Matching for Generative Modeling

arXiv 2210.02747 ↗First posted 6 Oct 2022cs.LG cs.AI stat.MLcited by 5,426

On the map: World models → Video-generation world models and simulators

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Abstract (arXiv)

We introduce a new paradigm for generative modeling built on Continuous Normalizing Flows (CNFs), allowing us to train CNFs at unprecedented scale. Specifically, we present the notion of Flow Matching (FM), a simulation-free approach for training CNFs based on regressing vector fields of fixed conditional probability paths. Flow Matching is compatible with a general family of Gaussian probability paths for transforming between noise and data samples -- which subsumes existing diffusion paths as specific instances. Interestingly, we find that employing FM with diffusion paths results in a more robust and stable alternative for training diffusion models. Furthermore, Flow Matching opens the door to training CNFs with other, non-diffusion probability paths. An instance of particular interest is using Optimal Transport (OT) displacement interpolation to define the conditional probability paths. These paths are more efficient than diffusion paths, provide faster training and sampling, and result in better generalization. Training CNFs using Flow Matching on ImageNet leads to consistently better performance than alternative diffusion-based methods in terms of both likelihood and sample quality, and allows fast and reliable sample generation using off-the-shelf numerical ODE solvers.

Key facts. Cited by 5,426 papers in the map (data through 7 Oct 2026). Placed in Video-generation world models and simulators, one of 11 directions in World models. Builds on 45 of its 67 references that are in the map. First posted on arXiv 6 Oct 2022.

Builds on

45 of 67 references.

Closest ancestors · 2

Same direction, newest first

  1. 2020Score-Based Generative Modeling through Stochastic Differential Equations26 Nov
  2. 2020Denoising Diffusion Probabilistic Models19 Jun

Other references · 43

  1. 2019PyTorch: An Imperative Style, High-Performance Deep Learning Librarycited by 20,160
  2. 2021High-Resolution Image Synthesis with Latent Diffusion Modelscited by 18,694
  3. 2020Denoising Diffusion Implicit Modelscited by 9,655
  4. 2021Diffusion Models Beat GANs on Image Synthesiscited by 8,185
  5. 2015Deep Unsupervised Learning using Nonequilibrium Thermodynamicscited by 7,005
  6. 2022Hierarchical Text-Conditional Image Generation with CLIP Latentscited by 6,539
  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. 2022Flow Straight and Fast: Learning to Generate and Transfer Data with Rectified Flowcited by 3,550
  11. 2018Glow: Generative Flow with Invertible 1x1 Convolutionscited by 1,539
  12. 2021Image Super-Resolution via Iterative Refinementcited by 1,506
31 more
  1. 2019Normalizing Flows for Probabilistic Modeling and Inferencecited by 1,315
  2. 2021Variational Diffusion Modelscited by 1,145
  3. 2022Building Normalizing Flows with Stochastic Interpolantscited by 964
  4. 2021Maximum Likelihood Training of Score-Based Diffusion Modelscited by 670
  5. 2020NVAE: A Deep Hierarchical Variational Autoencodercited by 635
  6. 2021Diffusion Schr"odinger Bridge with Applications to Score-Based Generative Modelingcited by 594
  7. 2018FFJORD: Free-form Continuous Dynamics for Scalable Reversible Generative Modelscited by 584
  8. 2022Fast Sampling of Diffusion Models with Exponential Integratorcited by 526
  9. 2019Augmented Neural ODEscited by 396
  10. 2017A Downsampled Variant of ImageNet as an Alternative to the CIFAR datasetscited by 374
  11. 2020Very Deep VAEs Generalize Autoregressive Models and Can Outperform Them on Imagescited by 261
  12. 2019Flow++: Improving Flow-Based Generative Models with Variational Dequantization and Architecture Designcited by 258
  13. 2019Residual Flows for Invertible Generative Modelingcited by 256
  14. 2020How to train your neural ODE: the world of Jacobian and kinetic regularizationcited by 228
  15. 2022Riemannian Score-Based Generative Modellingcited by 216
  16. 2020The Computational Limits of Deep Learningcited by 188
  17. 2020TrajectoryNet: A Dynamic Optimal Transport Network for Modeling Cellular Dynamicscited by 155
  18. 2020OT-Flow: Fast and Accurate Continuous Normalizing Flows via Optimal Transportcited by 143
  19. 2021Instance-Conditioned GANcited by 119
  20. 2017PacGAN: The power of two samples in generative adversarial networkscited by 104
  21. 2021Deep Generative Learning via Schr"odinger Bridgecited by 103
  22. 2021Soft Truncation: A Universal Training Technique of Score-based Diffusion Model for High Precision Score Estimationcited by 95
  23. 2020Interacting particle solutions of Fokker-Planck equations through gradient-log-density estimationcited by 87
  24. 2020Learning Differential Equations that are Easy to Solvecited by 81
  25. 2021Moser Flow: Divergence-based Generative Modeling on Manifoldscited by 67
  26. 2022Matching Normalizing Flows and Probability Paths on Manifoldscited by 57
  27. 2019High-Fidelity Image Generation With Fewer Labelscited by 51
  28. 2019Potential Flow Generator with L2 Optimal Transport Regularity for Generative Modelscited by 31
  29. 2017Logo Synthesis and Manipulation with Clustered Generative Adversarial Networkscited by 20
  30. 2021Partition-Guided GANscited by 9
  31. 2022TO-FLOW: Efficient Continuous Normalizing Flows with Temporal Optimization adjoint with Moving Speedcited by 8

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Cited by year (2026 to 7 Oct)

Citing papers per year: 2022: 6; 2023: 123; 2024: 494; 2025: 1858; 2026: 2945.

5,426 papers.

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  1. 2024Scaling Rectified Flow Transformers for High-Resolution Image Synthesiscited by 4,094
  2. 2025Wan: Open and Advanced Large-Scale Video Generative Modelscited by 2,536
  3. 2024π0: A Vision-Language-Action Flow Model for General Robot Controlcited by 2,297
  4. 2025π0.5: a Vision-Language-Action Model with Open-World Generalizationcited by 1,653
  5. 2024HunyuanVideo: A Systematic Framework For Large Video Generative Modelscited by 1,597
  6. 2025GR00T N1: An Open Foundation Model for Generalist Humanoid Robotscited by 1,167
  7. 2025FLUX.1 Kontext: Flow Matching for In-Context Image Generation and Editing in Latent Spacecited by 960
  8. 2023Stochastic Interpolants: A Unifying Framework for Flows and Diffusionscited by 897
  9. 2025Emerging Properties in Unified Multimodal Pretrainingcited by 855
  10. 2025Fine-Tuning Vision-Language-Action Models: Optimizing Speed and Successcited by 844
  11. 2023Improving and generalizing flow-based generative models with minibatch optimal transportcited by 835
  12. 2025Cosmos World Foundation Model Platform for Physical AIcited by 833
38 more
  1. 2024Structured 3D Latents for Scalable and Versatile 3D Generationcited by 742
  2. 2023Neural Codec Language Models are Zero-Shot Text to Speech Synthesizerscited by 737
  3. 2024SiT: Exploring Flow and Diffusion-based Generative Models with Scalable Interpolant Transformerscited by 707
  4. 2025Qwen2.5-Omni Technical Reportcited by 704
  5. 2024Representation Alignment for Generation: Training Diffusion Transformers Is Easier Than You Thinkcited by 666
  6. 2024Open-Sora: Democratizing Efficient Video Production for Allcited by 637
  7. 2025Flow-GRPO: Training Flow Matching Models via Online RLcited by 605
  8. 2025Self Forcing: Bridging the Train-Test Gap in Autoregressive Video Diffusioncited by 569
  9. 2024LTX-Video: Realtime Video Latent Diffusioncited by 549
  10. 2025Mean Flows for One-step Generative Modelingcited by 524
  11. 2025SmolVLA: A Vision-Language-Action Model for Affordable and Efficient Roboticscited by 507
  12. 2024Transfusion: Predict the Next Token and Diffuse Images with One Multi-Modal Modelcited by 468
  13. 2026World Action Models are Zero-shot Policiescited by 411
  14. 2025DanceGRPO: Unleashing GRPO on Visual Generationcited by 388
  15. 2023InstaFlow: One Step is Enough for High-Quality Diffusion-Based Text-to-Image Generationcited by 387
  16. 2023Voicebox: Text-Guided Multilingual Universal Speech Generation at Scalecited by 373
  17. 2024One Step Diffusion via Shortcut Modelscited by 373
  18. 2024Pyramidal Flow Matching for Efficient Video Generative Modelingcited by 354
  19. 2024F5-TTS: A Fairytaler that Fakes Fluent and Faithful Speech with Flow Matchingcited by 353
  20. 2025Hunyuan3D 2.0: Scaling Diffusion Models for High Resolution Textured 3D Assets Generationcited by 342
  21. 2024OminiControl: Minimal and Universal Control for Diffusion Transformercited by 334
  22. 2024SANA: Efficient High-Resolution Image Synthesis with Linear Diffusion Transformerscited by 331
  23. 2024DiffusionDrive: Truncated Diffusion Model for End-to-End Autonomous Drivingcited by 324
  24. 2024Discrete Flow Matchingcited by 301
  25. 2024Generative Flows on Discrete State-Spaces: Enabling Multimodal Flows with Applications to Protein Co-Designcited by 294
  26. 2023Understanding Diffusion Objectives as the ELBO with Simple Data Augmentationcited by 293
  27. 2026Causal World Modeling for Robot Controlcited by 289
  28. 2024Open-Sora Plan: Open-Source Large Video Generation Modelcited by 286
  29. 2025X-VLA: Soft-Prompted Transformer as Scalable Cross-Embodiment Vision-Language-Action Modelcited by 285
  30. 2024CosyVoice 2: Scalable Streaming Speech Synthesis with Large Language Modelscited by 282
  31. 2025π*0.6: a VLA That Learns From Experiencecited by 280
  32. 2025ReCamMaster: Camera-Controlled Generative Rendering from A Single Videocited by 278
  33. 2024Fast High-Resolution Image Synthesis with Latent Adversarial Diffusion Distillationcited by 276
  34. 2024Simplifying, Stabilizing and Scaling Continuous-Time Consistency Modelscited by 276
  35. 2025Diffusion Transformers with Representation Autoencoderscited by 275
  36. 2023Multisample Flow Matching: Straightening Flows with Minibatch Couplingscited by 267
  37. 2025Improving Video Generation with Human Feedbackcited by 267
  38. 2025MAGI-1: Autoregressive Video Generation at Scalecited by 262

50 most cited of 5,426 All 5,426 (JSON)

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  1. 2024Convergence Analysis of Flow Matching in Latent Space with Transformers
  2. 2025A Theoretical Analysis of Discrete Flow Matching Generative Models
  3. 2026Path-independent Flow Matching for Multi-parameter Generative Dynamics
  4. 2026Isokinetic Flow Matching for Pathwise Straightening of Generative Flows
  5. 2025Flow Matching: Markov Kernels, Stochastic Processes and Transport Plans
  6. 2025Graph Flow Matching: Enhancing Image Generation with Neighbor-Aware Flow Fields