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Mean Flows for One-step Generative Modeling

English reading report: Method, equations, original figures, experiments and reproducibility.

Authors: Zhengyang Geng; Mingyang Deng; Xingjian Bai; J. Zico Kolter; Kaiming He

Affiliations: CMU; MIT

Source: NeurIPS 2025 · ref-ce6916f81594a9c4c73f ↗ · Catalog record

Reading: 387 / 558 · 6 original figures & tables · ~19 min ·

1. Paper overview

In one sentence: Learning an interval-average velocity turns trajectory integration into a single prediction, at the cost of a derivative-based training target and configuration-sensitive optimization. e02e03e04e06e08e11e21

At a glanceWhat to know
Research problem
Source description

Straight sample-conditioned interpolation paths can induce curved marginal trajectories. A coarse numerical step using instantaneous velocity therefore misses the required displacement even with an accurate velocity field. The paper asks whether learning an interval-average field can make one-step generation effective without teacher distillation or a discretization curriculum. e02e03e01

Core mechanism
Source description

Defines average velocity independently of a neural network and derives the MeanFlow Identity linking it to instantaneous velocity. Appendix B.3 uses the zero-displacement boundary at equal times to establish sufficiency. e03e18

A key reported resultClass-conditional ImageNet 256×256 generation: 3.43

FID-50K (lower is better). FID on 50,000 generated images; XL/2, 676M parameters, 240 epochs, learned CFG, 1 NFE. Exact FID reference split/statistics are not identified in Sections 5 and A.

Shortcut-XL/2: 10.60 at 1 NFE; IMM-XL/2: 7.77 at one step but 2 NFE because of guidance. Strong reported improvement within the listed one-step diffusion/flow comparisons; these literature rows do not establish matched training budgets or statistical significance. e08e11e14e21

Reading caution
Source description

The checklist explicitly reports single-run FID-50K without variance estimates and acknowledges that limitations are not discussed comprehensively. Curated images cannot establish typical failure frequency or coverage. e20e21

Core contributions

  • Source description

    Defines average velocity independently of a neural network and derives the MeanFlow Identity linking it to instantaneous velocity. Appendix B.3 uses the zero-displacement boundary at equal times to establish sufficiency. e03e18

  • Source description

    Trains the average-velocity predictor with a Jacobian-vector product (JVP) and a detached regression target, then incorporates classifier-free guidance into training so sampling retains one function evaluation. e04e06

Figure 3. Average velocity follows an interval's displacement rather than a local tangent. Original paper, p. 4 ↗

Excerpt from the authors’ paper; cropped without altering the figure or table.

How to read it. Start at the left panel: purple arrows follow the curved path, while the orange arrow is parallel to the chord joining the marked times r and t. Multiplying average velocity u by t-r produces that chord's displacement. The remaining panels show that the relevant average field changes as the upper endpoint t changes. The arrows are drawn in the increasing-time direction. Equation (12) uses the same displacement with a minus sign when sampling backward from noise at t to an earlier r. Thus the graphic and sampling rule agree; an arrow pointing toward t should not be read as the generation direction. e03e05e18

What it supports. The desired prediction is an integral summarized per unit time. An accurate u can therefore replace many local velocity evaluations for the chosen interval. This geometric change explains why MeanFlow conditions its field on two times, even though generation can request only the single interval from 1 to 0.

Where the evidence stops. These are schematic fields, not measured trajectories of trained ImageNet models. The identity describes the exact target field; approximation quality and optimization success require experimental evidence.

2. Motivation

2.1 The problem and the proposed response

Source description

Straight sample-conditioned interpolation paths can induce curved marginal trajectories. A coarse numerical step using instantaneous velocity therefore misses the required displacement even with an accurate velocity field. The paper asks whether learning an interval-average field can make one-step generation effective without teacher distillation or a discretization curriculum. e02e03e01

2.2 What this reading follows

A flow model usually tells a sampler which direction to move at the current instant. MeanFlow asks for the average direction and magnitude over the whole remaining interval. The distinction matters because even straight data-to-noise interpolation paths can induce curved marginal trajectories. Its training rule derives an average-velocity target from an instantaneous velocity and a network derivative, avoiding a teacher trajectory solver. Guidance is also incorporated into training. Read the diagrams first to understand the displacement, then the algorithm and ablations to see how it is learned. The ImageNet headline is 3.43 FID with one generator evaluation; the pretrained VAE and single-run evaluation remain part of that result's scope. e02e03e04e06e08e11e21

3. Research context

We place the paper in the collection through its world–action interface. The catalog labels and the reading’s assessment are shown separately.

Catalog dimensionRecorded classification
Major categoryFoundational work
ArchitectureNot applicable
Prediction paradigmNot applicable
QuadrantNot applicable

3.1 Evidence-based assessment

Supports the recorded classification

Reader analysis

The catalog's foundational diffusion/flow-matching placement is supported. The architecture/prediction/quadrant fields are appropriately not applicable to the world-action taxonomy: a single image generator predicting average velocity does not establish a unified world-and-action model, joint future/action prediction or inverse-dynamics control. e03e05e08e13e14

This is the collection’s architectural analysis, not a new related-work survey. Benchmark comparisons and their protocols appear in Section 6.

4. Problem formulation

4.1 Inputs and outputs

InputsOutputs
  • Training data x, Gaussian noise epsilon, times r and t; class label for ImageNet guidance (e04, e06).
  • ImageNet: pretrained-VAE latents of size 32×32×4; CIFAR-10: 32×32×3 pixels (e08, e15).
  • An average-velocity prediction u_theta(z_t,r,t), converted into a generated latent or pixel sample by subtracting the interval displacement (e03, e05).

4.2 Equations and their role

u(zt,r,t)=1t−r∫rtv(zτ,τ) dτ,u=v−(t−r)dudtu(z_t,r,t)=\frac{1}{t-r}\int_r^t v(z_\tau,\tau)\,d\tau,\qquad u=v-(t-r)\frac{d u}{dt}
Here z_t is a flow state, r and t delimit the interval, tau is integration time, v is instantaneous marginal velocity, and u is average velocity. Differentiation holds r fixed and follows the trajectory. The equal-time limit is u=v. e03
utgt=vt−(t−r)(vt∂zuθ+∂tuθ),L(θ)=E∥uθ−sg⁡(utgt)∥22u_{\mathrm{tgt}}=v_t-(t-r)\left(v_t\partial_z u_\theta+\partial_t u_\theta\right),\qquad \mathcal{L}(\theta)=\mathbb{E}\left\|u_\theta-\operatorname{sg}(u_{\mathrm{tgt}})\right\|_2^2
Theta denotes network parameters; v_t is the sample-conditioned velocity. The partial derivatives form the JVP along (v_t,0,1); sg stops gradients through the target, avoiding higher-order optimization. This is the basic squared-error objective before adaptive weighting. e04e17
zr=zt−(t−r)uθ(zt,r,t),z0=ϵ−uθ(ϵ,0,1)z_r=z_t-(t-r)u_\theta(z_t,r,t),\qquad z_0=\epsilon-u_\theta(\epsilon,0,1)
The model predicts forward displacement per unit time, while generation moves from noise at t=1 toward data at r=0 by subtraction. Epsilon is the sampled Gaussian prior. e05

5. Method in detail

5.1 Why average velocity removes an integration problem

Reader analysis

Flow Matching begins with easily sampled data/noise pairs, but the learned field averages over pairs that can pass through the same noisy state. That marginal field need not trace a straight path. Consequently, even an exact instantaneous prediction can be a poor approximation to a large displacement. MeanFlow defines a different target: integrate the marginal velocity over an interval and divide by its duration. The network receives both interval endpoints because different endpoints generally imply different averages. Its prediction is still a velocity-shaped tensor, but multiplying it by the interval produces displacement. The reader's interpretation is that MeanFlow moves the burden of trajectory integration into learning the target field. This changes the approximation task; it does not guarantee that the finite network learns the exact integral. e02e03e05e18

Algorithms 1 and 2. Training computes the derivative correction; sampling uses one subtraction. Original paper, p. 5 ↗

Excerpt from the authors’ paper; cropped without altering the figure or table.

How to read it. Read Algorithm 1 from the interpolation z to the JVP call. Its first output is the network prediction u; its second is the total time derivative dudt. In input coordinates (z,r,t), the tangent (v,0,1) moves z along velocity, holds r fixed and advances t. The target subtracts the interval times this derivative from v. The stopgrad marker applies to the complete target: optimization differentiates the prediction branch but does not backpropagate through the target's JVP. Algorithm 2 then removes all these training operations. It draws noise and subtracts the predicted average velocity over the full interval. e04e05e06e07e08e17e19

What it supports. The extra derivative is a training cost, while the generated sample requires one call to fn. At t=r the correction becomes zero, connecting the method to Flow Matching. Appendix B.4 measures about 16% additional training wall time for one JAX B/4 benchmark on v4-8 TPUs.

Where the evidence stops. The pseudocode shows the unguided core and leaves time sampling and the loss metric abstract. ImageNet training additionally uses the guidance target, adaptive weights and pretrained VAE; one NFE is not a complete image-decoding latency measurement.

5.2 How a derivative supplies an integral target

Source description

Directly supervising the integral would require trajectories that the training loop wants to avoid computing. Differentiate the defining displacement with respect to the upper time while holding the lower time fixed. The product rule gives the average velocity plus an interval-scaled derivative; the integral derivative gives the instantaneous velocity. Rearranging yields the target form used in Algorithm 1. The total derivative includes both motion through state space and explicit time dependence, which explains the JVP tangent (v,0,1). Replacing the unknown field derivative by the current network derivative creates a self-dependent regression target. Detaching that target avoids higher-order parameter gradients. Equal-time samples remove the correction, while unequal-time samples exercise interval prediction. Table 1 tests both this sampling mixture and deliberately incorrect tangents. e03e04e09

Table 4. The recipe changes along with model size and training duration. Original paper, p. 21 ↗

Excerpt from the authors’ paper; cropped without altering the figure or table.

How to read it. Read each model as a column. The first block specifies architecture; the middle block gives training duration and shared optimizer settings; the final blocks specify interval learning and guidance. Centered shared entries apply across the relevant columns, rather than indicating missing values. The B/4 column points to the main ablation panels for settings varied there. Distinguish effective guidance omega' from omega in the target: Appendix B.1 relates them through kappa. The bottom row gives the time interval in which guidance is triggered. These rows are essential when comparing XL/2 with XL/2+, despite their identical parameter counts. e11e14e16e08e19

What it supports. XL/2+ keeps 676M parameters but trains for 1000 epochs instead of 240 and changes its guidance recipe. The reported two-evaluation improvement from 2.93 to 2.20 therefore combines longer training with configuration changes. A reproduction that only increases epochs would not match the specified experiment.

Where the evidence stops. Table 4 does not isolate the effects of those changes. It also does not identify random seeds, exact software versions, the FID reference-statistics artifact or the intermediate time used for two-step sampling.

5.3 How guidance changes the meaning of one step

Source description

Ordinary classifier-free guidance combines conditional and unconditional predictions during sampling, so one sampling step can require two evaluations. MeanFlow instead defines a guided instantaneous field and learns its corresponding average field. Training uses same-time network predictions inside the target, and Appendix B.1 mixes conditional and unconditional terms through kappa. The trained sampler then requests the guided average directly. This is why the paper separates IMM's one-step, two-evaluation row from one-evaluation rows. The reader should also separate evaluation count from training cost: a JVP is needed during training, and model-specific guidance windows alter the recipe. The strongest two-evaluation number belongs to the longer-trained XL/2+ variant. Finally, ImageNet's pretrained VAE remains a dependency even when the generator itself is trained from scratch. e06e08e11e14e16e19

5.4 Training and inference

During training

Source description

The generator is trained from scratch without a distilled teacher or curriculum; ImageNet nevertheless depends on a pretrained VAE. Standard ImageNet models use 240 epochs, Adam, batch 256, constant learning rate 0.0001, beta=(0.9,0.95), EMA 0.9999 and no weight decay. B/4 ablations use 80 epochs; XL/2+ uses 1000. e01e08e14

Source description

Sample two logit-normal times, order them, and enforce a mixture with 25% unequal-time pairs by default. Adaptive weighting uses a detached inverse power of squared regression error, with default p=1. Guidance parameters and active time intervals vary by model size. e07e14e17

During inference

Source description

Draw Gaussian z_1 and evaluate u_theta(z_1,0,1) once; subtract the prediction to obtain z_0. The latent-space output requires VAE decoding for an image. Guided sampling uses the learned guided field without a separate conditional/unconditional combination. The same interval update supports multiple steps; it executes no environmental action or feedback loop. e05e06e08

5.5 Implementation flow

  1. Construct a noisy training point

    Interpolate data and noise as z_t=(1-t)x+t epsilon. The accessible sample-conditioned velocity is v_t=epsilon-x; the marginal field averages conditional velocities compatible with z_t. e02e04

  2. Represent the interval

    ImageNet uses unchanged DiT/ViT blocks with adaLN-Zero conditioning. Each time variable receives a positional embedding and two-layer MLP; the embeddings are summed. Default conditioning is time t and interval t-r. e07e14

  3. Form a local derivative target

    Evaluate the network and its JVP along (v_t,0,1) in input coordinates (z,r,t). Subtract (t-r) times this derivative from v_t and regress against the detached target. At r=t the correction vanishes, recovering Flow Matching. e04

  4. Build guidance into the target

    The guided model replaces sample velocity by a mixture involving same-time conditional/unconditional predictions. Appendix B.1 introduces mixing coefficient kappa and effective guidance scale omega'=omega/(1-kappa). Class conditioning is dropped with probability 0.1. e06e16

6. Experiments & results

MeanFlow learns the average velocity between two times, allowing a noise sample to cross an entire generative flow in one network evaluation. A differential identity supplies a training target without integrating trajectories or distilling a teacher. Classifier-free guidance is learned into the field. ImageNet results are strong, but the pretrained latent tokenizer, single-run evaluation and configuration changes qualify the headline claims (e03–e06, e08, e11, e14, e21).

6.1 Read the original evidence

Figure 4. Longer training improves each plotted model; the largest reaches 3.43 FID. Original paper, p. 9 ↗

Excerpt from the authors’ paper; cropped without altering the figure or table.

How to read it. The horizontal axis is training epochs, not inference steps. Every curve retains one generator evaluation at inference. Follow a color across epochs to see improvement with longer training, then compare the labeled 240-epoch endpoints across model sizes. Table 2 on the same page confirms those values and supplies external comparisons: Shortcut has 10.60 FID at one evaluation, while IMM has 7.77 at one step with two evaluations for guidance. These are different efficiency categories. The figure's original vertical range excludes some early values above the plot; the crop preserves that original range and does not infer hidden endpoints. e08e11e12e14e21e23

What it supports. At 240 epochs, the reported B/2, M/2, L/2 and XL/2 FIDs are 6.17, 5.01, 3.84 and 3.43. The method remains effective at larger scales instead of losing its one-evaluation behavior. The evidence concerns image-distribution quality under the reported training recipes.

Where the evidence stops. Model size comparisons also change guidance settings in Table 4. Epochs do not equal matched compute, and no error bars are reported. Separately, Table 2 lists SiT at 2.06 while the preceding prose says 2.15; neither value is silently substituted for the other.

Figure 5. Curated one-evaluation examples show recognizable objects and fine textures. Original paper, p. 23 ↗

Excerpt from the authors’ paper; cropped without altering the figure or table.

How to read it. Inspect these as selected outputs from the class-conditional XL/2 model, not as a sequence of states or a set of held-out input/output pairs. The grid includes animals, vegetation, food and landscapes, allowing a reader to examine different kinds of texture and scene structure. For example, feathers, petals and fur provide visually distinct detail, while mountain and coastal scenes test a different scale of composition. The caption identifies this model with the 3.43-FID result and explicitly calls the examples curated. That selection statement matters as much as the apparent quality of any individual tile. e20e11e21

What it supports. The examples demonstrate that the one-evaluation generator can produce visually detailed and recognizable images across the displayed categories. They provide a qualitative companion to the aggregate ImageNet FID result, making the output type concrete without adding a new quantitative claim.

Where the evidence stops. No random sampling protocol or failure rate accompanies this grid. Its visual variety does not measure distributional coverage, class accuracy, memorization or typical quality; the authors' curated selection limits those conclusions.

6.2 Results and evaluation conditions

Task & protocolReported resultComparison & interpretation
Class-conditional ImageNet 256×256 generation

FID on 50,000 generated images; XL/2, 676M parameters, 240 epochs, learned CFG, 1 NFE. Exact FID reference split/statistics are not identified in Sections 5 and A.

3.43

FID-50K (lower is better)

Shortcut-XL/2: 10.60 at 1 NFE; IMM-XL/2: 7.77 at one step but 2 NFE because of guidance.

Strong reported improvement within the listed one-step diffusion/flow comparisons; these literature rows do not establish matched training budgets or statistical significance. e08e11e14e21

Two-evaluation ImageNet generation

Class-conditional ImageNet 256×256, FID-50K, learned CFG; standard XL/2 versus longer-trained XL/2+.

2.93 for XL/2; 2.20 for XL/2+

FID-50K (lower is better)

Table 2 lists DiT-XL/2 at 2.27 and SiT-XL/2 at 2.06, both 250×2 NFE.

XL/2+ uses 1000 epochs and different guidance settings, so its improvement is not an isolated sampling-step effect. Section 5.2 instead states SiT 2.15; this unresolved source discrepancy is preserved. e11e12e14

Average-velocity and JVP ablations

ImageNet 256×256, B/4, 80 epochs, no CFG, 1 NFE; Table 1a–b.

61.06 with 25% unequal-time pairs and tangent (v,0,1)

FID-50K (lower is better)

Equal-time-only Flow Matching: 328.91. Wrong tangents (v,0,0), (v,1,0), (v,1,1): 268.06, 329.22, 137.96.

Supports interval training and the correct total derivative in this setup. Deliberately invalid tangents are destructive controls, not competitive methods. e08e09

Unconditional CIFAR-10 generation

32×32 pixels; approximately 55M-parameter U-net; 1 NFE; FID on 50,000 generated images. Exact reference statistics are not stated.

2.92

FID-50K (lower is better)

iCT: 2.83; sCT: 2.97; IMM: 3.20. Competitors use EDM preconditioning; MeanFlow does not.

Competitive rather than uniformly best. CIFAR training and architecture differ from the ImageNet experiment. e13e15

6.3 Ablations and diagnostic examples

Read component removals and qualitative examples within their stated evaluation conditions.

Table 1a–f. Interval training and the correct derivative dominate the small-model diagnostic. Original paper, p. 8 ↗

Excerpt from the authors’ paper; cropped without altering the figure or table.

How to read it. All six panels use ImageNet 256×256, B/4, 80 training epochs and FID on 50,000 generated images with one evaluation. Gray marks the default settings. Compare within each panel, rather than treating its rows as stages of one cumulative recipe. Panel (a) varies how often r differs from t; panel (b) intentionally changes the JVP tangent. Panels (c) through (e) test representation and optimization choices. Panel (f) introduces guidance into the otherwise unguided default. Its omega sweep uses the basic guidance formulation, with kappa=0; it is not the improved mixing experiment of Appendix Table 5. e04e08e09e10e16e21

What it supports. Allowing 25% unequal-time pairs lowers FID from 328.91 to 61.06. Using (v,0,0) instead of (v,0,1) raises it to 268.06. Guidance at omega=3 reaches 15.53. Together these results support the interval correction and show that the final quality also depends strongly on guidance.

Where the evidence stops. The incorrect tangents are destructive controls. They establish sensitivity to the derivative calculation, not superiority over optimized alternative objectives. Results are single-run scores and use a smaller, shorter-trained backbone than the headline model.

7. Analysis & limitations

7.1 What the evidence leaves open

Source description

The checklist explicitly reports single-run FID-50K without variance estimates and acknowledges that limitations are not discussed comprehensively. Curated images cannot establish typical failure frequency or coverage. e20e21

Reader analysis

The identity constrains an ideal field; its sufficiency proof does not guarantee convergence of the finite network with a detached, self-dependent target. Image synthesis evidence does not validate physical dynamics, video prediction or action execution. e04e18e08e13

7.2 Questions for discussion

  1. How closely does a trained finite network satisfy interval additivity on held-out states?
  2. How much of the scaling advantage survives matched guidance settings and repeated training seeds?

8. Reproducibility audit

8.1 Requirements and known gaps

Source description

A faithful ImageNet attempt requires the referenced VAE, DiT conditioning, Table 4 configuration and forward-mode JVP with target detachment. Appendix B.4 reports JAX B/4 timing on v4-8 TPUs: 0.052 seconds/iteration versus Flow Matching's 0.045, approximately 16% overhead; this is not an end-to-end sampling speedup. e04e14e19

Reader analysis

The PDF does not pin software versions, random seeds or the exact FID reference-statistics artifact. Two-step intermediate times are not specified in the displayed configuration. Code-release statements also differ: page 16 says released, whereas page 19 plans release after acceptance. Availability remains unverified here. e08e14e19e22

8.2 Proposed reproduction checks

The following checks are proposals motivated by the paper. They have not been run as part of this reading.

Check 1: Verify the derivative before testing one-step FID

Reader-proposed, not executed: on a fixed minibatch and network, compare the JVP along (v,0,1) with a central finite difference that perturbs z along v, advances t and holds r fixed. Reduce the finite-difference step until numerical precision limits agreement. Then train paired B/4 runs using the correct tangent and the destructive (v,0,0) control, keeping data order, initialization, 25% unequal-time pairs, 80 epochs, loss weighting and no-CFG evaluation fixed. Evaluate FID-50K over multiple seeds. Derivative disagreement would reveal an implementation error; agreement without a consistent FID advantage would weaken the reported mechanism result in the replicated setting. e04e08e09e14e21

Check 2: Separate guidance mixing from guidance strength

Reader-proposed, not executed: repeat Table 5 with effective guidance omega'=2 fixed, comparing kappa=0 and kappa=0.9 while setting omega=(1-kappa)omega'. Match the B/4 architecture, training duration, class-drop probability, guidance interval, optimizer and evaluation inputs across runs. Use one generator evaluation for every sampled image and report seed-wise FID-50K rather than only a best score. The source reports 20.15 versus 18.63; a persistent improvement would support target mixing beyond merely increasing guidance strength. If the advantage disappears under repeats, the original single-run difference would not establish robustness. Log target components to verify that changing kappa has not accidentally changed the effective scale. e06e08e10e14e16e21

8.3 Reading coverage

Visual audit: Inspected the title and author block; Figures 1–5; Algorithms 1–2; Tables 1–5; method equations and training/evaluation text; checklist limitations, statistical and release statements; and Appendix A/B configuration, guidance, loss, sufficiency and JVP timing details. All six final source crops were viewed, including the corrected ablation crop and final scaling crop. Figure 3 arrow directions agree with the forward displacement definition and backward sampling subtraction; Algorithm 1's tangent and stop-gradient agree with Eqs. (8)–(11). Table 2 was visually read although Figure 4 is the selected main-result crop. Table 1 provides the original quantitative ablation table; Table 4 provides the configuration table. Text-reading covers all seven chunks and all 23 PDF pages; reference pages and remaining checklist boilerplate were not part of the image pass. Separate supplements, external code and referenced assets were not inspected.

PDF pages inspected for this edition: 1, 2, 3, 4, 5, 6, 7, 8, 9, 14, 16, 19, 21, 22, 23. Appendix coverage: reviewed.

Original figures and tables remain the work of the source’s authors. Extractions preserve their scientific content; any HTML wrapper layout is disclosed with each figure. The surrounding reading notes are our own.

Text reading scope & known omissions
  • Abstract
  • 1 Introduction
  • 2 Related Work
  • 3 Background: Flow Matching
  • 4 MeanFlow Models
  • 4.1 Mean Flows
  • 4.2 Mean Flows with Guidance
  • 4.3 Design Decisions
  • 5 Experiments
  • 5.1 Ablation Study
  • 5.2 Comparisons with Prior Work
  • 6 Conclusion
  • Acknowledgments
  • References
  • NeurIPS Paper Checklist (items 1–16)
  • Appendix A Implementation
  • B.1 Improved CFG for MeanFlow
  • B.2 Loss Metrics
  • B.3 On the Sufficiency of the MeanFlow Identity
  • B.4 Analysis on Jacobian-Vector Product (JVP) Computation
  • C Qualitative Results

Outside the original text pass

  • Text extraction does not reconstruct figure images; inspect the retained PDF for figures and equation/table layout.
  • Separate supplemental material availability has not been fully verified.
  • The extraction limitation was addressed by inspecting original PDF pages and all six final crops. All seven supplied text chunks were read individually; no supplied body or appendix text was omitted.
  • Identity/version note: the title and five-author identity match the catalog. The observed title page credits J. Zico Kolter, abbreviated to Zico Kolter in the catalog, and lists CMU and MIT. This report reviews the supplied 23-page NeurIPS 2025 proceedings edition; no numbered revision or revision date is established, and no earlier edition was compared (e01).
  • Code, linked assets, checkpoints and separate supplements were not inspected; no experiments were run. PDF pages containing references and checklist boilerplate were text-read, while the declared visual pass covers pages supporting retained claims.

The visual audit above records the subsequent illustrated pass.

8.4 Traceable evidence

e01PDF p. 1, title/author block, venue footer and abstractInspect

Exact title; Zhengyang Geng, Mingyang Deng, Xingjian Bai, J. Zico Kolter and Kaiming He; affiliations CMU and MIT; NeurIPS 2025. Abstract states generator training without pretraining, distillation or curriculum.

Go to primary source ↓
e02PDF pp. 2–3, Section 3, Figure 2 and Eqs. (1)–(2)Inspect

Linear data/noise interpolation supplies conditional velocity; marginalization can produce curved paths, motivating concern about coarse ODE integration.

Go to primary source ↓
e03PDF pp. 3–4, Section 4.1, Figure 3 and Eqs. (3)–(6)Inspect

Average velocity is integrated instantaneous velocity divided by interval length; differentiating with r fixed yields the MeanFlow Identity. The figure depicts forward displacement, not the subtraction used in generation.

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e04PDF pp. 4–5, Eqs. (7)–(11) and Algorithm 1Inspect

Total derivative uses input tangent (v,0,1); sample-conditioned velocity substitutes for the marginal velocity. The regression target is detached, avoiding differentiation through the JVP during parameter optimization.

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e05PDF p. 5, Sampling, Eq. (12) and Algorithm 2Inspect

Interval sampling subtracts (t-r)u from z_t; one-step sampling subtracts u(epsilon,0,1) from Gaussian noise.

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e06PDF p. 6, Section 4.2, Eqs. (13)–(19)Inspect

Guidance defines a modified underlying field and target. Class dropout is 10%; the learned guided average field supports sampling without an extra CFG evaluation.

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e07PDF pp. 7–8, Section 4.3 and Section 5.1 Time SamplersInspect

Uniform and logit-normal time sampling, ordering of the two times, equal-time mixture, alternative time embeddings and adaptive loss weights are described.

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e08PDF p. 7, Section 5 Experiment SettingInspect

ImageNet 256×256 uses pretrained-VAE 32×32×4 latents and FID over 50K generated images. B/4 ablations train for 80 epochs (400K iterations). The paragraph does not name a FID reference-statistics artifact.

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e09PDF p. 8, Table 1a–b and overall captionInspect

B/4, 80 epochs, 1-NFE FID: unequal-time ratios 0/25/50/100% yield 328.91/61.06/63.14/67.32. Correct tangent gives 61.06; three incorrect tangents give 268.06, 329.22 and 137.96.

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e10PDF p. 8, Table 1c–fInspect

Default time/interval embedding and logit-normal(-0.4,1.0) give 61.06. Loss p=0 gives 79.75 versus p=1 at 61.06. CFG omega=3 gives 15.53, versus 61.06 without CFG; this table uses no improved kappa mixing.

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e11PDF p. 9, Table 2, all rows and captionInspect

MeanFlow XL/2: 3.43 at 1 NFE, 2.93 at 2 NFE; XL/2+: 2.20 at 2 NFE. Shortcut: 10.60 at 1 NFE; IMM: 7.77 at 1×2 NFE. DiT: 2.27; SiT: 2.06 at 250×2 NFE. Caption identifies longer/configuration-adjusted XL/2+ and iCT numbers reported by IMM.

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e12PDF p. 8, Section 5.2 final paragraph; p. 9, Table 2 SiT-XL/2 rowInspect

The prose gives SiT FID 2.15, whereas Table 2 gives 2.06. The supplied edition does not resolve the discrepancy.

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e13PDF p. 9, Table 3 and CIFAR-10 ComparisonsInspect

CIFAR-10 unconditional pixel generation uses the same approximately 55M U-net family; 1-NFE FID-50K is 2.92 for MeanFlow, 2.83 iCT, 2.97 sCT, 3.20 IMM and 3.60 ECT. Other rows use EDM preconditioning.

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e14PDF p. 21, Appendix A, Table 4 and ImageNet paragraphInspect

DiT blocks, adaLN-Zero and summed two-time embeddings; VAE reference in footnote 4. Table gives architecture, optimizer, durations, loss, time sampling and model-specific guidance. XL/2 has 676M parameters, 240 epochs, effective scale 2.5, omega 0.2 and guidance interval [0,0.75]; XL/2+ uses 1000 epochs, scale 2, omega 1 and interval [0.3,0.8].

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e15PDF p. 21, Appendix A, CIFAR-10 paragraphsInspect

CIFAR uses pixel U-net inputs, concatenated time embeddings and no EDM preconditioner; training uses 800K iterations, 10K warm-up, learning rate 0.0006, batch 1024, 75% unequal-time pairs and p=0.75.

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e16PDF p. 22, Appendix B.1, Eqs. (20)–(21), Table 5Inspect

Target mixes sample velocity with conditional and unconditional same-time outputs. Effective guidance is omega/(1-kappa). At effective scale 2, FID changes from 20.15 at kappa=0 to 18.63 at kappa=0.9; Table 1f used kappa=0.

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e17PDF p. 22, Appendix B.2, Eq. (22)Inspect

Regression-error-dependent weight is 1/(squared error+c)^p, with positive stabilizer c; the weight is detached before multiplying squared error.

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e18PDF pp. 22–23, Appendix B.3, Eqs. (23)–(24)Inspect

Displacement S=(t-r)u vanishes at equal times, fixing the integration constant in the sufficiency argument; directly parameterizing arbitrary displacement would need an additional boundary condition.

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e19PDF p. 23, Appendix B.4Inspect

JVP uses forward-mode autodiff with stop-gradient. JAX B/4 timing on v4-8 TPUs is 0.045 seconds/iteration for Flow Matching and 0.052 for MeanFlow, reported as 16% overhead. Software versions and seeds are not specified here.

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e20PDF p. 23, Figure 5 and Appendix CInspect

Figure shows explicitly curated class-conditional ImageNet 256×256 samples from MeanFlow-XL/2 with 1 NFE and reported FID 3.43.

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e21PDF p. 14, checklist item 2; p. 16, checklist item 7Inspect

Authors answer No to comprehensive limitations discussion and to statistical-significance reporting. They explicitly identify single-run FID-50K scores without variance estimates.

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e22PDF p. 1, abstract code link; p. 16, checklist item 5; p. 19, checklist item 13Inspect

Abstract links code and item 5 says complete source/environment instructions are released; item 13 says code and checkpoints are planned after acceptance and absent from the submission package. These are source statements, not inspected availability.

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e23PDF p. 9, Figure 4 and Table 2 MeanFlow B/2–XL/2 rowsInspect

The 1-NFE scaling plot shows lower FID with longer training; 240-epoch endpoints are 6.17, 5.01, 3.84 and 3.43 for B/2, M/2, L/2 and XL/2, respectively.

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8.5 Primary sources

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