mlsanityData to 7 Oct 2026

Flow Straight and Fast: Learning to Generate and Transfer Data with Rectified Flow

arXiv 2209.03003 ↗First posted 7 Sep 2022cs.LGcited by 3,550

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

Abstract (arXiv)

We present rectified flow, a surprisingly simple approach to learning (neural) ordinary differential equation (ODE) models to transport between two empirically observed distributions π0 and π1, hence providing a unified solution to generative modeling and domain transfer, among various other tasks involving distribution transport. The idea of rectified flow is to learn the ODE to follow the straight paths connecting the points drawn from π0 and π1 as much as possible. This is achieved by solving a straightforward nonlinear least squares optimization problem, which can be easily scaled to large models without introducing extra parameters beyond standard supervised learning. The straight paths are special and preferred because they are the shortest paths between two points, and can be simulated exactly without time discretization and hence yield computationally efficient models. We show that the procedure of learning a rectified flow from data, called rectification, turns an arbitrary coupling of π0 and π1 to a new deterministic coupling with provably non-increasing convex transport costs. In addition, recursively applying rectification allows us to obtain a sequence of flows with increasingly straight paths, which can be simulated accurately with coarse time discretization in the inference phase. In empirical studies, we show that rectified flow performs superbly on image generation, image-to-image translation, and domain adaptation. In particular, on image generation and translation, our method yields nearly straight flows that give high quality results even with a single Euler discretization step.

Key facts. Cited by 3,550 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 75 of its 100 references that are in the map. First posted on arXiv 7 Sep 2022.

Builds on

75 of 100 references.

References · 75

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38 more
  1. 2018Neural Ordinary Differential Equationscited by 3,733
  2. 2021GLIDE: Towards Photorealistic Image Generation and Editing with Text-Guided Diffusion Modelscited by 3,595
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50 most cited of 75 All 75 (JSON)

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Cited by year (2026 to 7 Oct)

Citing papers per year: 2022: 12; 2023: 123; 2024: 393; 2025: 1259; 2026: 1763.

3,550 papers.

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  1. 2022Flow Matching for Generative Modelingcited by 5,426
  2. 2023Consistency Modelscited by 1,778
  3. 2025GR00T N1: An Open Foundation Model for Generalist Humanoid Robotscited by 1,167
  4. 2023One-step Diffusion with Distribution Matching Distillationcited by 978
  5. 2025Qwen-Image Technical Reportcited by 973
  6. 2022Building Normalizing Flows with Stochastic Interpolantscited by 964
  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. 2023Improving and generalizing flow-based generative models with minibatch optimal transportcited by 835
  11. 2023Latent Consistency Models: Synthesizing High-Resolution Images with Few-Step Inferencecited by 826
  12. 2024Structured 3D Latents for Scalable and Versatile 3D Generationcited by 742
38 more
  1. 2023Adversarial Diffusion Distillationcited by 741
  2. 2024SiT: Exploring Flow and Diffusion-based Generative Models with Scalable Interpolant Transformerscited by 707
  3. 2024Representation Alignment for Generation: Training Diffusion Transformers Is Easier Than You Thinkcited by 666
  4. 2025Flow-GRPO: Training Flow Matching Models via Online RLcited by 605
  5. 2025Self Forcing: Bridging the Train-Test Gap in Autoregressive Video Diffusioncited by 569
  6. 2025Mean Flows for One-step Generative Modelingcited by 524
  7. 2023Consistency Trajectory Models: Learning Probability Flow ODE Trajectory of Diffusioncited by 448
  8. 2023Improved Techniques for Training Consistency Modelscited by 430
  9. 2026World Action Models are Zero-shot Policiescited by 411
  10. 2024From Slow Bidirectional to Fast Autoregressive Video Diffusion Modelscited by 401
  11. 2024OmniGen: Unified Image Generationcited by 388
  12. 2025DanceGRPO: Unleashing GRPO on Visual Generationcited by 388
  13. 2023InstaFlow: One Step is Enough for High-Quality Diffusion-Based Text-to-Image Generationcited by 387
  14. 2025Reconstruction vs. Generation: Taming Optimization Dilemma in Latent Diffusion Modelscited by 376
  15. 2024One Step Diffusion via Shortcut Modelscited by 373
  16. 2024Pyramidal Flow Matching for Efficient Video Generative Modelingcited by 354
  17. 2024Retrieval-Augmented Generation for AI-Generated Content: A Surveycited by 352
  18. 2025Hunyuan3D 2.0: Scaling Diffusion Models for High Resolution Textured 3D Assets Generationcited by 342
  19. 2024DiffusionDrive: Truncated Diffusion Model for End-to-End Autonomous Drivingcited by 324
  20. 2024Discrete Flow Matchingcited by 301
  21. 2024Generative Flows on Discrete State-Spaces: Enabling Multimodal Flows with Applications to Protein Co-Designcited by 294
  22. 2026Causal World Modeling for Robot Controlcited by 289
  23. 2022Rectified Flow: A Marginal Preserving Approach to Optimal Transportcited by 277
  24. 2024Fast High-Resolution Image Synthesis with Latent Adversarial Diffusion Distillationcited by 276
  25. 2024Simplifying, Stabilizing and Scaling Continuous-Time Consistency Modelscited by 276
  26. 2025Diffusion Transformers with Representation Autoencoderscited by 275
  27. 2023Multisample Flow Matching: Straightening Flows with Minibatch Couplingscited by 267
  28. 2025Improving Video Generation with Human Feedbackcited by 267
  29. 2025MAGI-1: Autoregressive Video Generation at Scalecited by 262
  30. 2023Flow Matching on General Geometriescited by 260
  31. 2024SDXL-Lightning: Progressive Adversarial Diffusion Distillationcited by 258
  32. 2022EDICT: Exact Diffusion Inversion via Coupled Transformationscited by 256
  33. 2025Z-Image: An Efficient Image Generation Foundation Model with Single-Stream Diffusion Transformercited by 247
  34. 2025Show-o2: Improved Native Unified Multimodal Modelscited by 242
  35. 2025OmniGen2: Towards Instruction-Aligned Multimodal Generationcited by 241
  36. 2023SinSR: Diffusion-Based Image Super-Resolution in a Single Stepcited by 235
  37. 2023Diff-Instruct: A Universal Approach for Transferring Knowledge From Pre-trained Diffusion Modelscited by 232
  38. 2025SAM 3D: 3Dfy Anything in Imagescited by 230

50 most cited of 3,550 All 3,550 (JSON)

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  4. 2026Path-independent Flow Matching for Multi-parameter Generative Dynamics
  5. 2025Flow Matching: Markov Kernels, Stochastic Processes and Transport Plans
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