Overcoming the Curvature Bottleneck in MeanFlow

Xinxi Zhang*, Shiwei Tan*, Quang Nguyen, Quan Dao, Ligong Han, Xiaoxiao He, Tunyu Zhang
Chengzhi Mao, Dimitris Metaxas, Vladimir Pavlovic
Rutgers University
* Equal Contribution
ARXIV GITHUB

The Curvature Bottleneck

Meanflow offers a promising framework for one-step generative modeling by directly learning a mean-velocity field, bypassing expensive numerical integration. The challenge, however, lies in the geometry of the trajectory itself. Under the standard independent data-noise coupling, these trajectories are highly curved. We argue that this curvature is a key bottleneck for efficient mean-velocity modeling: intuitively, learning the mean velocity on a straight trajectory is much easier than learning it on a curved one. Motivated by this observation, we propose Re-MeanFlow, which learns the mean-velocity field on rectified, straighter trajectories. By addressing the curvature bottleneck, Re-MeanFlow enables substantially more efficient mean-velocity modeling.

Flow Trajectory
Trajectory Curvature
Straight Curved
Trajectory Curvature

Re-MeanFlow

MeanFlow learns the mean-velocity field under the standard independent coupling \(p(\mathbf{x},\mathbf{z}) = p(\mathbf{x})\,p(\mathbf{z})\), whose induced generative trajectories are known to be highly curved. Re-MeanFlow instead trains on a rectified coupling, where each noise sample \(\mathbf{z}\) is paired with a data sample \(\mathbf{x}\) obtained by solving the transport process with a pretrained flow model, analogous to the reflow procedure in Rectified Flow. This rectified pairing produces substantially straighter trajectories, making the mean-velocity field much easier to learn.

MeanFlow on Curved Trajectory Re-MeanFlow on Rectified Trajectory
Re-MeanFlow method: rectifying curved trajectories to simplify the curvature landscape

Curvature surfaces \(\mathrm{Curv}(r,t)\) are computed from real generative trajectories on ImageNet, with
\(\mathrm{Curv}(r,t)=\mathbb{E}_{\mathbf{z}_t\sim p_t}\!\Big[\angle\!\big(u(\mathbf{z}_t,r,t),\,v(\mathbf{z}_t,t)\big)\Big]\).

Smoother Landscape, Faster Convergence

Straighter trajectories make mean-velocity learning dramatically easier. With the same initialization, Re-MeanFlow converges substantially faster than MeanFlow. Visualizing the loss landscape along two PCA directions reveals why: MeanFlow exhibits a rugged, sharply peaked landscape, whereas Re-MeanFlow is markedly smoother and better conditioned, making optimization significantly easier.

MeanFlow Loss Landscape Re-MeanFlow Loss Landscape Convergence Speed (FID vs GPU Hours)
Loss landscape comparison and convergence speed

Results

Compared to prior state-of-the-art flow-based one-step methods, Re-MeanFlow achieves the best FID across all settings on ImageNet, outperforming both one-step distillation and training-from-scratch methods on class-conditional ImageNet generation.

ImageNet 64×64
MethodNFEFID
Diffusion models
EDM2-S63 × 21.58
 + Autoguidance63 × 21.01
EDM2-XL63 × 21.33
Few-step models
2-rectified flow++14.31
iCT14.02
ECD-S13.30
sCD-S12.97
TCM12.88
AYF12.98
Re-MeanFlow (ours)12.87
ImageNet 256×256
MethodNFEFID
Diffusion models
ADM250 × 210.94
DiT-XL250 × 22.27
SiT-XL250 × 22.06
SiT-XL + REPA250 × 21.42
Few-step models
iCT134.6
SM110.6
iSM15.27
iMM1 × 27.77
MeanFlow13.43
Re-MeanFlow (ours)13.41
ImageNet 512×512
MethodNFEFID
Diffusion models
EDM2-S63 × 22.23
 + Autoguidance63 × 21.34
EDM2-XXL63 × 21.81
Few-step models
ECT19.98
ECD18.47
CMT13.38
sCT-S110.13
sCD-S13.07
AYF13.32
Re-MeanFlow (ours)13.03
Re-MeanFlow one-step generation samples on ImageNet

One-step generation (NFE=1) on ImageNet at 64×64 (left), 256×256 (middle), and 512×512 (right).

BibTeX

@misc{zhang2026overcomingcurvaturebottleneckmeanflow,
      title={Overcoming the Curvature Bottleneck in MeanFlow}, 
      author={Xinxi Zhang and Shiwei Tan and Quang Nguyen and Quan Dao and Ligong Han and Xiaoxiao He and Tunyu Zhang and Chengzhi Mao and Dimitris Metaxas and Vladimir Pavlovic},
      year={2026},
      eprint={2511.23342},
      archivePrefix={arXiv},
      primaryClass={cs.CV},
      url={https://arxiv.org/abs/2511.23342}, 
}