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home / papers / 2022 / Flow Straight and Fast: Learning to Generate and Transfer Data with Rectified Flow

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

Written for the Research library (claude-opus-5-5) from the paper text, in our own words: the license "arXiv — non-exclusive license to distribute" does not allow redistributing the text itself. Original — arxiv.org/pdf/2209.03003

Summary

Many learning tasks reduce to finding a map that carries one distribution onto another: generating images from noise, translating between image domains, or adapting a model to shifted test data. Existing approaches have drawbacks. GANs train unstably, likelihood-based models are often intractable, and diffusion models are slow at inference because they need many solver steps. The authors propose rectified flow, a neural ODE whose velocity field is fit by plain least-squares regression to the direction of straight segments joining random pairs of samples from the two distributions. ODE trajectories cannot cross, so the learned flow reorganises intersecting segments into a deterministic coupling. They prove this never increases any convex transport cost. Repeating the procedure on pairs produced by the previous flow ("reflow") makes paths progressively straighter, so they can be integrated with very few Euler steps, even a single one. Experiments cover CIFAR10 generation, translation among animal and face datasets, and domain adaptation. The work matters because it handles generation and transfer in one simple, scalable framework and narrows the speed gap between one-step and continuous-time models.

Key points

  • One-step generation: After one reflow, the 2-rectified flow produces good images with a single Euler step. On CIFAR10 the authors report FID 4.85 and recall 0.51, which they claim as state of the art among one-step diffusion/flow models.
  • Training: The objective adds no parameters beyond ordinary supervised learning. Because it is time-symmetric, the same model can be run forward (π0→π1) or backward (π1→π0).
  • Image-to-image translation: Experiments use pairs drawn from AFHQ, MetFace and CelebA-HQ at 512×512, with an 80/20 train/test split. A classifier-feature-weighted loss steers which style attributes get transferred.
  • Domain adaptation: The flow is applied to latent features of a pre-trained model, using the DDPM++ architecture and 100 uniform steps. Accuracy is 69.2 on OfficeHome versus 68.7 for Deep CORAL, and 41.4 on DomainNet versus 41.5 for CORAL. This is on par with or better than ERM, IRM, ARM, Mixup and MLDG.
  • Image editing: Inverting the ODE gives a latent code that can be moved toward high-probability regions of the Gaussian, either by scaling or by Langevin-style updates. This turns unnatural stitched images into realistic ones.

Our summary of the paper, in our own words — not its text. The work belongs to its authors; read it at the links above.

Fields: Other

Cited by

173 papers of our library cite it (of the 140673 whose bibliographies we read); 1 of them have a page here, 172 not yet.

Cite

The paper itself, not this page. BibTeX from the library's record of the work. DOI 10.48550/arxiv.2209.03003 · arXiv 2209.03003

@misc{liu2022flow,
  title = {{Flow Straight and Fast: Learning to Generate and Transfer Data with Rectified Flow}},
  author = {Liu, Xingchao and Gong, Chengyue and Liu, Qiang},
  year = {2022},
  doi = {10.48550/arxiv.2209.03003},
  eprint = {2209.03003},
  archivePrefix = {arXiv},
  url = {https://doi.org/10.48550/arxiv.2209.03003}
}

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