mlsanityData to 7 Oct 2026

Consistency Flow Matching: Defining Straight Flows with Velocity Consistency

arXiv 2407.02398 ↗First posted 2 Jul 2024cs.CVcited by 101

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

Abstract (arXiv)

Flow matching (FM) is a general framework for defining probability paths via Ordinary Differential Equations (ODEs) to transform between noise and data samples. Recent approaches attempt to straighten these flow trajectories to generate high-quality samples with fewer function evaluations, typically through iterative rectification methods or optimal transport solutions. In this paper, we introduce Consistency Flow Matching (Consistency-FM), a novel FM method that explicitly enforces self-consistency in the velocity field. Consistency-FM directly defines straight flows starting from different times to the same endpoint, imposing constraints on their velocity values. Additionally, we propose a multi-segment training approach for Consistency-FM to enhance expressiveness, achieving a better trade-off between sampling quality and speed. Preliminary experiments demonstrate that our Consistency-FM significantly improves training efficiency by converging 4.4x faster than consistency models and 1.7x faster than rectified flow models while achieving better generation quality. Our code is available at: https://github.com/YangLing0818/consistency_flow_matching

Key facts. Cited by 101 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 46 of its 53 references that are in the map. First posted on arXiv 2 Jul 2024.

Builds on

46 of 53 references.

Closest ancestors · 10

Same direction, newest first

  1. 2024Optimal Flow Matching: Learning Straight Trajectories in Just One Step19 Mar
  2. 2024Dirichlet Flow Matching with Applications to DNA Sequence Design8 Feb
  3. 2024Generative Flows on Discrete State-Spaces: Enabling Multimodal Flows with Applications to Protein Co-Design7 Feb
  4. 2023Bellman Optimal Stepsize Straightening of Flow-Matching Models27 Dec
  5. 2023InstaFlow: One Step is Enough for High-Quality Diffusion-Based Text-to-Image Generation12 Sep
  6. 2023Equivariant flow matching26 Jun
  7. 2023Multisample Flow Matching: Straightening Flows with Minibatch Couplings28 Apr
  8. 2023Improving and generalizing flow-based generative models with minibatch optimal transport1 Feb
  9. 2022Flow Matching for Generative Modeling6 Oct
  10. 2022Flow Straight and Fast: Learning to Generate and Transfer Data with Rectified Flow7 Sep

Other references · 36

  1. 2020Denoising Diffusion Probabilistic Modelscited by 20,851
  2. 2021High-Resolution Image Synthesis with Latent Diffusion Modelscited by 18,694
  3. 2020Denoising Diffusion Implicit Modelscited by 9,655
  4. 2020Score-Based Generative Modeling through Stochastic Differential Equationscited by 8,964
  5. 2023SDXL: Improving Latent Diffusion Models for High-Resolution Image Synthesiscited by 4,290
  6. 2024Scaling Rectified Flow Transformers for High-Resolution Image Synthesiscited by 4,094
  7. 2019Generative Modeling by Estimating Gradients of the Data Distributioncited by 4,067
  8. 2013Auto-Encoding Variational Bayescited by 3,980
  9. 2018Neural Ordinary Differential Equationscited by 3,733
  10. 2022Elucidating the Design Space of Diffusion-Based Generative Modelscited by 2,994
  11. 2017Progressive Growing of GANs for Improved Quality, Stability, and Variationcited by 2,967
  12. 2015Variational Inference with Normalizing Flowscited by 2,161
24 more
  1. 2016Density estimation using Real NVPcited by 2,029
  2. 2022DPM-Solver: A Fast ODE Solver for Diffusion Probabilistic Model Sampling in Around 10 Stepscited by 1,961
  3. 2023Consistency Modelscited by 1,778
  4. 2018Glow: Generative Flow with Invertible 1x1 Convolutionscited by 1,539
  5. 2022Diffusion Models: A Comprehensive Survey of Methods and Applicationscited by 1,107
  6. 2019StarGAN v2: Diverse Image Synthesis for Multiple Domainscited by 1,095
  7. 2022Building Normalizing Flows with Stochastic Interpolantscited by 964
  8. 2021Maximum Likelihood Training of Score-Based Diffusion Modelscited by 670
  9. 2021Score-based Generative Modeling in Latent Spacecited by 634
  10. 2021Tackling the Generative Learning Trilemma with Denoising Diffusion GANscited by 515
  11. 2023Consistency Trajectory Models: Learning Probability Flow ODE Trajectory of Diffusioncited by 448
  12. 2023Improved Techniques for Training Consistency Modelscited by 430
  13. 2022Analytic-DPM: an Analytic Estimate of the Optimal Reverse Variance in Diffusion Probabilistic Modelscited by 331
  14. 2019Residual Flows for Invertible Generative Modelingcited by 256
  15. 2023Diff-Instruct: A Universal Approach for Transferring Knowledge From Pre-trained Diffusion Modelscited by 232
  16. 2021Score-Based Generative Modeling with Critically-Damped Langevin Diffusioncited by 230
  17. 2024Mastering Text-to-Image Diffusion: Recaptioning, Planning, and Generating with Multimodal LLMscited by 224
  18. 2019Optimal transport mapping via input convex neural networkscited by 202
  19. 2022Fast Sampling of Diffusion Models via Operator Learningcited by 173
  20. 2022GENIE: Higher-Order Denoising Diffusion Solverscited by 127
  21. 2022Poisson Flow Generative Modelscited by 95
  22. 2023Minimizing Trajectory Curvature of ODE-based Generative Modelscited by 87
  23. 2021Densely connected normalizing flowscited by 49
  24. 2023A Comprehensive Survey on Knowledge Distillation of Diffusion Modelscited by 45

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Cited by year (2026 to 7 Oct)

Citing papers per year: 2024: 10; 2025: 50; 2026: 41.

101 papers.

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  1. 2025Mean Flows for One-step Generative Modelingcited by 524
  2. 2024Simplifying, Stabilizing and Scaling Continuous-Time Consistency Modelscited by 276
  3. 2024FlowPolicy: Enabling Fast and Robust 3D Flow-based Policy via Consistency Flow Matching for Robot Manipulationcited by 99
  4. 2024PnP-Flow: Plug-and-Play Image Restoration with Flow Matchingcited by 92
  5. 2025Align Your Flow: Scaling Continuous-Time Flow Map Distillationcited by 81
  6. 2024Rectified Diffusion: Straightness Is Not Your Need in Rectified Flowcited by 59
  7. 2025Can We Detect Failures Without Failure Data? Uncertainty-Aware Runtime Failure Detection for Imitation Learning Policiescited by 49
  8. 2025ManiFlow: A General Robot Manipulation Policy via Consistency Flow Trainingcited by 43
  9. 2025AlphaFlow: Understanding and Improving MeanFlow Modelscited by 40
  10. 2025Variational Rectified Flow Matchingcited by 34
  11. 2024Flow Generator Matchingcited by 26
  12. 2024SnapGen-V: Generating a Five-Second Video within Five Seconds on a Mobile Devicecited by 25
38 more
  1. 2025Training-free Diffusion Acceleration with Bottleneck Samplingcited by 25
  2. 2025Temporal Difference Flowscited by 20
  3. 2025The Curse of Conditions: Analyzing and Improving Optimal Transport for Conditional Flow-Based Generationcited by 16
  4. 2025VCT: Training Consistency Models with Variational Noise Couplingcited by 15
  5. 2025FreqPolicy: Efficient Flow-based Visuomotor Policy via Frequency Consistencycited by 13
  6. 2025Learning an Image Editing Model without Image Editing Pairscited by 13
  7. 2024Distilling Diffusion Models to Efficient 3D LiDAR Scene Completioncited by 10
  8. 2024Analyzing and Mitigating Model Collapse in Rectified Flow Modelscited by 10
  9. 2025WideRange4D: Enabling High-Quality 4D Reconstruction with Wide-Range Movements and Scenescited by 10
  10. 2025FlowerDance: MeanFlow for Efficient and Refined 3D Dance Generationcited by 10
  11. 2025VFP: Variational Flow-Matching Policy for Multi-Modal Robot Manipulationcited by 9
  12. 2025Efficient Image Restoration via Latent Consistency Flow Matchingcited by 8
  13. 2025Fast Flow-based Visuomotor Policies via Conditional Optimal Transport Couplingscited by 8
  14. 2025Taming Diffusion Transformer for Efficient Mobile Video Generation in Secondscited by 8
  15. 2026Image Generation with a Sphere Encodercited by 8
  16. 2025OAT-FM: Optimal Acceleration Transport for Improved Flow Matchingcited by 7
  17. 2026Mean-Flow based One-Step Vision-Language-Actioncited by 7
  18. 2026RC-NF: Robot-Conditioned Normalizing Flow for Real-Time Anomaly Detection in Robotic Manipulationcited by 7
  19. 2026Fast Image Super-Resolution via Consistency Rectified Flowcited by 7
  20. 2025Diffusion-Sharpening: Fine-tuning Diffusion Models with Denoising Trajectory Sharpeningcited by 6
  21. 2025Score Distillation of Flow Matching Modelscited by 6
  22. 2025Riemannian Consistency Modelcited by 6
  23. 2025AlignFlow: Improving Flow-based Generative Models with Semi-Discrete Optimal Transportcited by 6
  24. 2024YingSound: Video-Guided Sound Effects Generation with Multi-modal Chain-of-Thought Controlscited by 5
  25. 2025A Survey on Pre-Trained Diffusion Model Distillationscited by 5
  26. 2025Functional Mean Flow in Hilbert Spacecited by 5
  27. 2026FlowCorrect: Efficient Interactive Correction of Generative Flow Policies for Robotic Manipulationcited by 5
  28. 2026One-Step Flow Policy: Self-Distillation for Fast Visuomotor Policiescited by 5
  29. 2025Universal Inverse Distillation for Matching Models with Real-Data Supervision (No GANs)cited by 4
  30. 2025EfficientFlow: Efficient Equivariant Flow Policy Learning for Embodied AIcited by 4
  31. 2025OMP: One-step Meanflow Policy with Directional Alignmentcited by 4
  32. 2026Path-Decoupled Hyperbolic Flow Matching for Few-Shot Adaptationcited by 4
  33. 2026From Flow to One Step: Real-Time Multi-Modal Trajectory Policies via Implicit Maximum Likelihood Estimation-based Distribution Distillationcited by 4
  34. 2025Train-Once Plan-Anywhere Kinodynamic Motion Planning via Diffusion Treescited by 3
  35. 2025Fast3Dcache: Training-free 3D Geometry Synthesis Accelerationcited by 3
  36. 2026FlowCast: Trajectory Forecasting for Scalable Zero-Cost Speculative Flow Matchingcited by 3
  37. 2026FastFlow: Accelerating The Generative Flow Matching Models with Bandit Inferencecited by 3
  38. 2026Formalizing the Sampling Design Space of Diffusion-Based Generative Models via Adaptive Solvers and Wasserstein-Bounded Timestepscited by 3

50 most cited of 101 All 101 (JSON)

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  1. 2026Exploring and Exploiting Stability in Latent Flow Matching
  2. 2026Stable Velocity: A Variance Perspective on Flow Matching
  3. 2024Improving Consistency Models with Generator-Augmented Flows
  4. 2024Flow map matching with stochastic interpolants: A mathematical framework for consistency models
  5. 2026Same Flow, Different Paths: Variance Reduction in Flow Matching
  6. 2025SCoT: Unifying Consistency Models and Rectified Flows via Straight-Consistent Trajectories
  7. 2025Generative Modeling with Continuous Flows: Sample Complexity of Flow Matching
  8. 2026VTV-FM: Flow Matching through Variational Terminal-Velocity Closure