Source
Geng, Deng, Bai, Kolter and He (2025), LIT-784 — MeanFlow, §4, Tables 1–3 and App. B.4.
What to do
If you need a one- or two-step generator and have no pretrained diffusion or flow model to distil from, train one directly as a MeanFlow model:
- The network takes two times, u_θ(z_t, r, t), and predicts the average velocity over [r, t], the displacement divided by t − r.
- Regress it onto u_tgt = v − (t − r)·(v·∂_z u_θ + ∂_t u_θ), with the target under stop-gradient. Here v is the conditional flow-matching velocity ε − x, and the bracket is one Jacobian-vector product with tangent (v, 0, 1).
- Use r ≠ t on a minority of samples (25% was best), sample (r, t) from a logit-normal, and use the adaptive loss weight with p = 1 (SOTA-443).
- Fold classifier-free guidance into the target, so a guided sample still costs one evaluation.
- Sample in one step: x = ε − u_θ(ε, 0, 1).
With r = t on every sample the objective is plain flow matching. The second time is what makes one step work.
Evidence
Against the other from-scratch one-step models (LIT-784, Table 2, ImageNet-256, DiT-XL/2 size, with guidance):
| Method | NFE | FID | Budget |
|---|---|---|---|
| iCT (re-run by Inductive Moment Matching) | 1 | 34.24 | as IMM ran it |
| Shortcut Models | 1 | 10.60 | 160–250 epochs at batch 256 |
| MeanFlow | 1 | 3.43 | 240 epochs at batch 256 |
| Inductive Moment Matching | 1 × 2 | 7.77 | about 3,800 epochs at batch 4,096 |
| MeanFlow | 2 | 2.93 | 240 epochs |
The budgets are not matched, and the mismatch mostly runs against MeanFlow. Inductive Moment Matching trained about sixteen times as many epochs. Shortcut Models’ XL run is about 160 passes over ImageNet by its appendix and 250 epochs by its own table (LIT-787). Either way it is close to MeanFlow’s 240.
The second time is the active ingredient (Table 1a, B/4, 80 epochs, one step, no guidance). With r = t always, FID is 328.91, which is flow matching. With r ≠ t on 25%, 50% and 100% of samples it is 61.06, 63.14 and 67.32. Wrong JVP tangents give 137.96 to 329.22 (Table 1b).
It scales (Table 2). One-step FID 6.17, 5.01, 3.84 and 3.43 for B/2, M/2, L/2 and XL/2.
It is cheap per step (App. B.4). The JVP’s output sits inside the stop-gradient, so there is no second-order backward pass. Measured cost is 0.052 against 0.045 s per iteration for flow matching, 16% more.
Conditions
- The alternatives were not re-run. Shortcut Models’ and Inductive Moment Matching’s rows are their own papers’ numbers. The iCT row is Inductive Moment Matching’s re-implementation, which that paper says “often collapses” (LIT-775). iCT at its own recipe has never been run on ImageNet-256.
- It is a better estimator, not a different target. THEORY-119 places MeanFlow’s identity as the Eulerian equation of the two-time flow map of the probability-flow ODE, the same object a shortcut model trains through composition and consistency training through the one-time Eulerian form. So the lead in the table above is a difference of estimator (identity, discretization, weighting and budget), not of what is being learned. The account holds no position on which estimator wins and does not explain this ranking; that still rests on the copied rows. Inductive Moment Matching is outside it, because its minimizer need not be the ODE’s map.
- On CIFAR-10 it is second to iCT (Table 3, one shared U-Net): MeanFlow 2.92 against iCT 2.83 in one step. It beats sCT’s 2.97, but sCT starts from a pretrained diffusion model (LIT-790, App. G), so that row is not from scratch. It also beats Inductive Moment Matching’s 3.20. The large ImageNet lead does not appear at 32 px.
- Not tested against train-then-distil. The paper frames itself as needing “no pre-training, distillation, or curriculum learning” and runs no distillation arm. Where a teacher already exists, the record’s evidence points elsewhere. rCM (LIT-783, App. F.1) shows MeanFlow’s objective is a continuous-time consistency trajectory model under the rectified-flow schedule, and finds it distils a large text-to-image model worse than plain sCM, in quality and diversity. That is one figure, run “without extensive hyperparameter tuning”.
- The step count is a weak dial. The average-velocity field admits any step count by construction, but only one and two steps are reported. That is thinner than the multi-step evidence behind SOTA-206 from Shortcut Models and Inductive Moment Matching.
- FID is the only metric. There is no precision, recall or diversity measure, guidance is folded into the model, and there is one run per row.
- Teacher-free one-step training is not easy in general. Flow map matching (LIT-793, §3.5) found learning the full one-step map directly “challenging”, and trained a short-interval map first. MeanFlow’s direct one-step training at ImageNet-256 has not been re-run by anyone else.
Known implementations
- MeanFlow, the source’s code.