Rethinking Prediction Horizons: Decoupling Model Queries from State Updates in Few-Step MeanFlow
MeanFlow normally couples the prediction horizon $h_k$ to the update step $\delta_k$. This paper decouples them, showing on CIFAR-10 that longer horizons hurt FID near the source $(t=0)$ but help at the midpoint $(t=0.5)$, and that this midpoint gain depends on earlier guidance choices. A frozen four-query rule improves mean FID by 2.0 without retraining or extra calls, yet ImageNet calibration finds no benefit beyond shifting query starts. The work establishes prediction horizon as a distinct but configuration-sensitive inference control.
The paper's central claim—that prediction horizon is a separately tunable, position-sensitive inference coordinate in few-step MeanFlow—is convincingly demonstrated on CIFAR-10 but faces sharp limits elsewhere. The authors report that 'the tested Horizon allocation adds no FID benefit beyond Grid+Start on two public ImageNet models' (Section 5.2) and that 'practical selection therefore remains target-dependent' (Section 6). The theoretical decomposition in Equation 5 separates horizon mismatch $\bar{v}_h(t) - \bar{v}_\delta(t)$ from interval-dependent prediction error $\epsilon_\theta$, yet it does not predict the observed sign reversal or provide a rule for selecting $h_k$, remaining descriptive rather than predictive.
The position-dependent sign reversal is the strongest empirical finding. Across seven independently trained CIFAR-10 checkpoints at CFG scale 2, extending a single horizon from $0.25$ to $0.50$ worsens endpoint FID at $t=0$ but improves it at $t=0.50$, and the authors note that 'the position scan is distinct from the 50k frozen-rule endpoint in Section 3' (Section 4.1). The incoming-state control is equally well-designed: by holding the midpoint query time fixed while changing only earlier CFG, they show that 'Mean horizon benefit rises from 0.109 to 1.308' (Section 4.2), establishing sensitivity to the incoming-state distribution beyond query time alone.
The primary limitation is narrow scope: the position reversal and incoming-state dependence are established within 'one guided CIFAR architecture and training recipe' (Section 6), and the theoretical analysis in Equation 5 and the Taylor expansion in Equation 8 explain that changing $h_k$ alters both horizon mismatch and prediction error, yet offer no way to predict the sign reversal or to select $h_k$ without target rollouts.
More critically, the calibrated comparisons reveal that horizon is often dominated by alternatives: on historical CIFAR at CFG 1.5, 'Horizon reduces FID relative to Local by 1.394, but Start reduces it by a further 0.566' (Section 5.1), and on public ImageNet models Grid+Start+Horizon 'has higher mean confirmation FID than Grid+Start' (Section 5.2). The frozen four-query rule was selected from eight binary schedules on a historical checkpoint (Appendix B.2), so despite being fixed before prospective confirmation, it remains a development-chosen configuration rather than a theoretically derived rule.
The evidence is strongest for class-conditional CIFAR-10, where 'FID and KID wins on 7/7 checkpoints' (Section 3.2) and gains persist on a stronger frozen grid. The matched-budget calibration—25 candidates with 10k paired development samples each—fairly shows that query-start shifts often outperform horizon changes: 'Start leads on FID, but evaluator rankings differ' (Section 5.1). The comparison to related work is accurate in distinguishing this fixed-interface, pretrained-model intervention from Decoupled MeanFlow's structural changes and from grid-optimization methods, though the framing of horizon as a distinct control understates that Start is usually the preferred one.
Reproducibility is unusually thorough. The appendices specify sampler contracts, training recipes with exact hyperparameters (EMA decay .999, AdamW $5\times10^{-4}$, effective batch 256), checkpoint provenance including SHA-256 prefixes, and paired-evaluation aggregation rules. The source package contains 'frozen protocols, per-cell reports and portable table renderers' (Reproducibility Statement). Nevertheless, full independent reproduction would be blocked by the idiosyncratic training pipeline—specifically the 'fixed map and online pairing' with a Hungarian-matched prototype system and a custom JVP loss with exponents like $S/(\operatorname{stopgrad} S + 10^{-3})^{.75}$ (Appendix A.2)—which is not standard or publicly validated. The manuscript does not release pretrained weights or standard dataset splits.
MeanFlow predicts interval-average velocities, but conventional few-step sampling ties the interval queried from the model to the duration of the state update. We separate these two quantities at inference, fixing the model, update grid, and number of queries while varying the prediction horizon. Our central finding is that the horizon response depends on both query position and the states entering that query. Across seven independently trained CIFAR-10 checkpoints at classifier-free guidance (CFG) scale 2, a longer horizon worsens FID at early steps but improves it at the midpoint. To probe whether query time alone determines this response, we fix the midpoint query and current/subsequent guidance while changing only earlier CFG. In held-out factorial outcomes on five previously studied checkpoints, the mean midpoint horizon benefit increases from 0.109 to 1.308 FID, indicating sensitivity to the incoming-state distribution. A frozen four-query rule reduces mean CIFAR-10 FID by 2.023 without retraining or extra queries, including gains on five checkpoints trained after rule selection. A milder rule also improves mean FID by 1.041 on a stronger frozen grid, with fixed-rule FID gains on the evaluated public ImageNet-256 and AFHQ checkpoints. However, matched-budget calibration favors query-start shifting in historical CIFAR tests, and the tested Horizon allocation adds no FID benefit beyond Grid+Start on two public ImageNet models. Thus, prediction horizon is a distinct, position- and state-sensitive inference control, but not a universally preferred one.
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