Overcoming the Curvature Bottleneck in MeanFlow

• Curved trajectories make few-step velocity approximation difficult, while the sharply peaked, irregular MeanFlow landscape contrasts with Re-MeanFlow’s smoother objective.The figure reports faster convergence and stronger one-step generation even when MeanFlow is trained for 2× longer.Source: §1 · p. 1, Figure 1 · p. 2
• Re-MeanFlow is a data-free self-distillation approach that trains MeanFlow on rectified couplings from a pretrained flow model, yielding straighter trajectories and a simpler mean-velocity learning problem.Source: §1 · p. 2
• A distance-based heuristic discards the top 10% of couplings by endpoint ℓ2 distance, removing residual high-curvature trajectories and improving training stability and sample quality.Source: §1 · pp. 2–3
• Re-MeanFlow reduces FID by 33.4% versus 2-rectified flow++ while using only 10% of the compute.Source: §1 · p. 3
• Across ImageNet at 642, 2562, and 5122, Re-MeanFlow outperforms state-of-the-art distillation methods and strong train-from-scratch baselines in quality and training efficiency.Source: §1 · p. 3
• Re-MeanFlow shifts most computation to inference-driven coupling generation and its training cost is 17% of the total GPU hours used by AYF [42].Source: §1 · p. 3

2 Related Work

• The review covers diffusion and flow methods that reduce sampling cost through trajectory straightening or few-step modeling, alongside advances in efficient training.Source: §2 · p. 3

2.1 Diffusion and Flow Matching.

• Diffusion and flow models reverse gradual noising through probability-flow ODEs, but high-curvature paths typically require multi-step numerical integration for sampling [46] [58].Source: §2.1 · p. 3

2.2 Straightening the Generative Trajectories.

• OT-inspired regularization and minibatch couplings reduce curvature, while Rectified Flow uses reflow to globally straighten trajectories; this work adopts rectified paths for MeanFlow training [51] [39] [31].Source: §2.2 · p. 3

2.3 Few-step Diffusion/Flow Models.

• Consistency and flow-map models bypass ODE integration, but learning mappings on curved trajectories can make supervision noisy and optimization difficult [11] [32] [47] [54] [5] [9] [10].Source: §2.3 · p. 4

2.4 Efficient Training for Diffusion/Flow Models.

• Efficiency work uses external representation learners, masked-token training, or progressive diffusion-to-consistency training; Re-MeanFlow instead supports one-step modeling on a simplified flow path [27] [52] [56] [37] [60] [11].Source: §2.4 · p. 4

3.1 One-Step Flow-Based Generative Modeling via MeanFlow

• MeanFlow models average velocity over [r, t] and samples with one evaluation, uθ(z, 0, 1), avoiding numerical ODE integration.The mean-velocity is defined as the time-average of the instantaneous velocity over the interval.Source: §3.1 · pp. 5–6

3.2 Taming the Curvature Bottleneck

• Curvature in the independent coupling complicates the mean-velocity target and creates a rugged objective; a single reflow step with a pretrained flow produces straighter trajectories and a smoother objective.The paper links the smoother objective to faster convergence and improved one-step generation.Source: §3.2 · p. 6

3.3 Estimating the Curvature of the Generative Trajectory

• Curv(r, t) averages the angle between interval-average transport direction and instantaneous velocity; perfectly straight trajectories have Curv(r, t) = 0 for all valid pairs.The proxy is estimated using a learned velocity field integrated under the corresponding coupling.Source: §3.3 · pp. 6–7

3.4 Training

• Rectification lowers average pair distance, but a residual long-distance tail is more curved; truncating the top 10% longest pairs targets these high-curvature couplings.The distance threshold is chosen by percentile and the top-10% truncation is reported to work robustly across settings.Source: Figure 3 · p. 8, Classifier-free guidance · p. 8
• For classifier-free guidance, training first proceeds without guidance and then uses a brief guidance fine-tuning stage; Re-MeanFlow typically converges within one pass over generated couplings.The paper reports the two-stage procedure as more stable in practice.Source: Classifier-free guidance · pp. 7–8

4 Experiments

• Experiments use ImageNet at 64², 256², and 512², with pretrained EDM2-S or SiT-XL initialization and comparisons against one-step methods selected for comparable architecture or compute.ImageNet-64² uses pixel space; the 256² and 512² experiments use latent space.Source: Datasets · p. 8, Settings · p. 9, Baselines · p. 9

4.1 One-Step Generation Quality

• Re-MeanFlow achieves the best FID across all ImageNet settings and reduces FID by 33.4% versus 2-rectified flow++ on ImageNet-642.The table covers class-conditional generation, using classifier-free guidance when supported.Source: Table 1 · p. 9, §4.1 · p. 10

4.2 Training Efficiency

• On ImageNet-512², Re-MeanFlow reaches FID 8.6 versus MeanFlow’s 30.9 despite MeanFlow receiving 2× the compute budget.Re-MeanFlow’s one-step samples closely match its multi-step samples, while MeanFlow’s remain noticeably blurry.Source: Compared to MeanFlow · p. 11
• Re-MeanFlow is 26.6× faster than 2-rectified flow++ in GPU hours and remains 2.9× faster than AYF.Re-MeanFlow has the lowest overall compute cost among recent distillation approaches; its coupling-sampling stage can run on inference-grade GPUs.Source: Compared to Other One-Step… · p. 12

4.3 Loss Landscape

• As t − r grows, MeanFlow’s loss landscape becomes sharper and more irregular, while Re-MeanFlow’s remains smoother and better-conditioned.The landscape is evaluated over a 2D grid spanning the top two PCA directions of z_t samples, with t fixed at 0.7.Source: §4.3 · pp. 12–13

4.4 Distance-based Truncation

• Discarding the top 10% of couplings by ℓ2 endpoint distance removes many residual high-curvature pairs and improves training stability and sample quality.Moderate truncation improves stability and sample quality while maintaining comparable diversity; FID improves monotonically within a moderate truncation regime.Source: §4.4 · pp. 13–14
• Even without truncation, Re-MeanFlow matches MeanFlow trained from scratch on real data while learning solely from generated coupling pairs.The authors hypothesize rectified trajectories simplify optimization despite the discretization error associated with self-generated distillation.Source: §4.4 · p. 14

4.5 Ablation Study

• The ImageNet-512² ablation reduces adaptive-loss normalization from 1.0 to 0.5, replaces the EDM2 time embedding and lognormal schedule, and excludes a high-variance time region.The study reports that excluding t > 0.95 and r < 0.4 improves FID and accelerates convergence; distance-based truncation further improves efficiency and generation quality.Source: §4.5 · p. 14, Table 3 · p. 14

5 Conclusion

• On ImageNet at 64², 256², and 512², Re-MeanFlow outperforms prior one-step flow distillation methods and strong Rectified Flow baselines with higher sample quality and substantially less training.The conclusion describes the framework as lightweight and data-free.Source: §5 · pp. 14–15
• Re-MeanFlow learns mean velocity on rectified couplings from a pretrained flow model, producing straighter trajectories and a better-conditioned loss landscape.A distance-based truncation rule removes residual high-curvature couplings to improve robustness.Source: §5 · p. 15

A More Discussion

• The paper’s discussion covers limitations, broader impact, the theoretical motivation for a single rectification iteration, and comparison with concurrent CMT [19].The supplied discussion passage identifies these topics but does not state the paper’s specific limitation.Source: A More Discussion · p. 19

A.1 Limitation

• Re-MeanFlow uses synthetic samples from pretrained diffusion or flow models, so performance depends on the quality of those generated couplings.The authors identify incorporating real data or improving the pretrained backbones as possible directions.Source: §A.1 · p. 19

A.2 Broader Impact

• Re-MeanFlow shifts substantial computation to inference-driven coupling generation, followed by lightweight training, reducing reliance on scarce high-end training GPUs.Coupling generation can run asynchronously alongside training, although this work pre-generates couplings; the authors report the lowest total compute among prior state-of-the-art distillation methods.Source: §A.2 · p. 20

A.3 Comparison with One-Step Sampling via Rectified Flow

• Unlike repeated reflow, which can be costly and accumulate approximation errors, Re-MeanFlow targets residual curvature after one rectification step to support stable one-step generation.The comparison notes that trajectories after one reflow are substantially straighter than independent couplings, but residual curvature can remain.Source: §A.3 · p. 20, Relation to Our Work · p. 21

A.4 Comparison with CMT

• CMT learns a trajectory-to-endpoint mapping in a mid-training stage, whereas Re-MeanFlow distills rectified endpoint couplings in one training stage.The authors say this avoids CMT’s two-stage optimization complexity and sensitivity to hyperparameters at both stages.Source: §A.4 · p. 21

B Implementation Details

• Training settings for Re-MeanFlow across ImageNet resolutions are provided in Table 4.The section first outlines pretrained-model conditioning and key training choices.Source: B Implementation Details · p. 21, Table 4 · p. 22

B.1 Pretrained Model Conditioning

• Re-MeanFlow uses separate t and r embeddings, initialized to preserve pretrained behavior; EDM2-S uses a short alignment stage, while SiT-XL receives a zero-initialized r embedding.The EDM2-S alignment trains the new embeddings to reproduce the original time-embedding output; its stated setup uses 10k iterations at learning rate 1e-3.Source: §B.1 · p. 22, On ImageNet 642 and 5122 · p. 22, On ImageNet 2562 · pp. 22–23

B.2 Time Distribution

• The authors use a U-shaped distribution for t and an AYF-style interval-length draw, while uniform t sampling is also competitive and often beats common log-normal distributions.They attribute uniform sampling’s strong performance to lower variance in rectified trajectories, which stabilizes early-time and high-noise regions.Source: §B.2 · p. 23

B.3 Avoiding High-Variance Time Regions

• For sampled pairs with t > 0.95 and r < 0.4, setting r = 0 improves training stability and FID and accelerates convergence.The authors hypothesize that predicting a clean target from near-pure noise is easier than predicting a lightly corrupted target at high t.Source: §B.3 · pp. 23–24

B.4 Training with Guidance

• For guidance, Re-MeanFlow trains on an improved CFG formulation, using an unconditional-flow stage before a CFG-modified stage.The authors report that direct CFG-field training is unstable; randomizing the effective guidance scale and using large κ also support stable training.Source: §B.4 · p. 24

C.1 Loss Landscape

• Across ImageNet resolutions, Re-MeanFlow’s loss landscape remains substantially smoother and better-conditioned than MeanFlow’s as the time interval varies.Figure 9 evaluates the loss on a PCA grid at t = 0.7 and r values from 0.7 to 0.1; the comparison covers ImageNet 64^2 and 256^2.Source: Figure 9 · p. 25

C More Experiment Details and Results

• The section also reports additional convergence results intended to support the synergy between trajectory rectification and mean-velocity modeling.It introduces loss-landscape visualizations and computational analyses as further experimental details.Source: C More Experiment Details and Results · pp. 24–25

C.1 Loss Landscape

• For additional resolutions, the analysis fixes t = 0.7, sweeps r, computes PCA directions from 20 k samples of zt (equivalently, xt), and evaluates LMF on a 2D grid spanned by the top two PCA directions.Source: §C.1 · p. 25

C.2 Computation Estimation of Each Method

• Training FLOPs are estimated from iteration count, batch size, forward and backward work, and GFLOPs per forward pass; sampling FLOPs use sample count, steps, and forwards per step.The accounting treats backward passes as approximately twice the cost of a forward pass.Source: FLOPS Estimation · p. 26
• For Re-MeanFlow on ImageNet-64^2, the example estimates about 64 EFLOPs for sampling and 8 EFLOPs for training.The sampling estimate uses five steps, two forward passes per step, and 102 GFLOPs per forward pass; training is calculated for two stages.Source: FLOPS Estimation · p. 26
• The AYF example estimates approximately 84 EFLOPs, counting training computation because AYF does not require sampling.The section computes GPU hours as the number of GPUs multiplied by wall-clock training time; Re-MeanFlow’s example is 528 GPU hours.Source: FLOPS Estimation · p. 26, GPU Hours Estimation · p. 27
• Across ImageNet 512^2 and 256^2, Re-MeanFlow converges markedly faster and reaches substantially lower FID than MeanFlow and related baselines.Figure 10 plots FID against training time measured in 8 × A100 GPU hours.Source: Figure 10 · p. 27

C.3 Additional Convergence Comparison with Other Related Methods

• 33.4% lower FID and 26× faster than 2-rectified flow++ are reported for Re-MeanFlow.The comparison concerns one-step sample quality and convergence efficiency.Source: 2-rectified flow++ · p. 27
• Mini-batch OT slightly improves over standard MeanFlow but still converges similarly and lags substantially behind Re-MeanFlow.The authors attribute this to local transport structure that does not guarantee globally straight trajectories.Source: MeanFlow with Mini-batch OT couplings · p. 28

C.4 Curvature Estimation

• Across ImageNet resolutions, rectified couplings induce substantially lower curvature over the (r, t)-plane than independent couplings.The additional estimates show the same trend as the ImageNet 512² comparison.Source: §C.4 · p. 28, Figure 11 · p. 28

D 2D Toy Example

• Re-MeanFlow produces more accurate one-step generation with fewer invalid samples than 2-rectified flow and MeanFlow in the 20k-iteration toy comparison.It uses 10k iterations to obtain a 1-rectified coupling, followed by 10k iterations of MeanFlow on those couplings.Source: D 2D Toy Example · p. 28, Figure 12 · p. 29
• 2-rectified flow retains one-step outliers because residual curvature can make instantaneous-velocity Euler updates overshoot.Some samples travel disproportionately long distances toward the denser mode, producing early-time curvature.Source: Figure 12d · p. 29, Figure 12 · p. 29
• MeanFlow trained directly on independent couplings fails to learn a coherent transport map within the same budget, while Re-MeanFlow combines rectification with mean-velocity modeling.The two components reduce curvature enough for efficient MeanFlow optimization and remove the requirement for perfectly straight trajectories.Source: D 2D Toy Example · p. 30, Figure 12e, Figure 12f
• Discarding the top 10% of couplings by endpoint distance yields cleaner one-step transport, with nearly all outliers removed in the toy task.The heuristic removes most high-curvature diagonal pairings but does not guarantee removal of every high-curvature path.Source: D 2D Toy Example · p. 30, Figure 13 · p. 30

E.1 ImageNet-642

• Selected qualitative Re-MeanFlow samples are shown for ImageNet 64².Source: Figure 14 · p. 31

E.2 ImageNet-2562

• Selected qualitative Re-MeanFlow samples are shown for ImageNet 256².Source: Figure 15 · p. 32

E.3 ImageNet-5122

• Selected qualitative Re-MeanFlow samples are shown for ImageNet 512².Source: Figure 16 · p. 33