Guidance Is a Field, Not a Scalar: Interval-Integrated Classifier-Free Guidance for One-Step Video Generation

Zijie Meng; Xixin Cao

cs.CVNov 5, 2026

Guidance Is a Field, Not a Scalar: Interval-Integrated Classifier-Free Guidance for One-Step Video Generation

Authors: Zijie Meng, Xixin Cao

Organizations: Peking University

Abstract

One-step generators built on MeanFlow synthesize a video in a single function evaluation, yet inherit a rigid treatment of classifier-free guidance (CFG): the guidance scale is frozen during training or, at best, exposed as a single scalar. This conflicts with mounting evidence that the optimal guidance is not a constant but a field that varies with the noise level, with spatial content, and, for video, with frame position. Every existing remedy presupposes a multi-step sampler along which guidance can be re-scheduled--an assumption one-step models violate by construction. We resolve this tension through a single observation: because the MeanFlow target is an integral over a noise interval, an arbitrary guidance field can be absorbed into the target itself and compiled into one evaluation. We formalize this as the interval-integrated CFG identity, prove that the compiled guidance carries no schedule-discretization error and can thus match or exceed any finite multi-step sampler, and instantiate it as AGAVE, which equips the average-velocity field with a learnable temporal schedule, a free motion-saliency spatial modulation, and a frame-position asymmetry. Adding fewer than ten scalars at zero inference cost, AGAVE surpasses all one-step baselines on VBench, UCF-101 and MSR-VTT while matching multi-step guided sampling. Project repository: https://github.com/YMlinfeng/AGAVE.

Figures & tables

Figure 1: Overview of AGAVE . A single MeanFlow DiT

\bm{u}_{\theta}

emits a conditional/unconditional velocity pair whose guidance gap

\Delta\bm{v}

is modulated along three axes – a learnable Beta schedule over noise level

\tau

, a free motion-saliency map

M

over space, and a learnable frame-position profile

\rho(f)

– forming a continuous guidance field

\omega(\bm{z}_{\tau},\tau,f)

. The interval-integrated CFG operator (Thm. 1 ) absorbs this field into the average-velocity target, compiling a full time-, space- and frame-varying schedule into one evaluation. The schedule parameters

\phi

are learned by distilling a multi-step adaptively guided teacher; inference remains strictly 1-NFE.

Figure 2: VBench 16-dimension radar (14B). AGAVE (filled) against the one-step baselines iMF, rCM and CFG-Zero ⋆ . The advantage is broad rather than localized and is widest on the motion-related axes; the lone axis where a baseline leads is background consistency.

Panel of Figure 3 — Figure 3: Interval-integrated CFG. The learnable Beta schedule $\omega(\tau)$ (red) vanishes at the high-noise end (zero-init) and peaks mid-interval. The average-velocity target integrates the whole schedule over $[r,t]$ (shaded), while the boundary term reads only the local value $\omega(t)$ (blue dot). One trained evaluation thus reproduces a continuously scheduled guidance.

Figure 4: Compilation gap. A

K

-step adaptive sampler only reaches the VBench total that AGAVE attains at

K{=}1

(dashed) as

K

grows, visualizing the

\Theta(1/K)

error of Prop. 1 .

Method	NFE	Total $\uparrow$	Quality $\uparrow$	Semantic $\uparrow$	Subj. Cons. $\uparrow$	Bg. Cons. $\uparrow$	Motion Smooth. $\uparrow$	Dynamic Degree $\uparrow$	Aesth. Qual. $\uparrow$
14B backbone
Wan2.1 teacher [ 40 ]	50	84.0	84.9	80.4	95.0	96.3	98.2	54.0	63.0
rCM [ 49 ]	4	85.0	85.6	80.9	95.3	96.5	98.4	53.5	62.9
rCM [ 49 ]	1	83.0	84.0	78.2	94.1	96.7	97.6	47.5	60.2
MeanFlow CFG [ 8 ]	1	83.3	84.2	78.7	94.3	95.9	97.7	49.0	60.8
CFG-Zero ⋆ (1-step) [ 6 ]	1	83.6	84.4	79.0	94.6	96.0	97.9	50.3	61.3

Table 1: VBench text-to-video on Wan2.1-distilled backbones (480p). Best and second-best among one-step methods. Amber rows are ours. AGAVE attains the best total at 1-NFE , surpassing even the 4-step teacher-level baseline and recovering the dynamic degree lost to uniform guidance.

Method	NFE	UCF FVD $\downarrow$	MSR-VTT FVD $\downarrow$	CLIP -T $\uparrow$	$+$ Par. $\times$ Lat.
Wan2.1 teacher	50	380	268	0.305	$\times$ 50
rCM (4-step)	4	372	262	0.307	$\times$ 4
rCM (1-step)	1	495	348	0.290	$\times$ 1
iMF	1	441	318	0.298	$\times$ 1
AGAVE	1	372	261	0.309	$+9$ $\times$ 1

Table 2: Zero-shot FVD, fidelity and cost (14B). AGAVE keeps the 1-NFE latency of rCM while matching multi-step quality, adding only a handful of scalars.

Figure 5: Recovered noise-time schedule. The learned

\omega(\tau)

(bold, inside the Beta family in light red) is bell-shaped and vanishes at the high-noise end, recovering the iMF constant (dashed) and the CFG-Zero ⋆ step (dotted) as special cases.

Figure 6: Learned frame-position profile.

\rho(f)

(line) peaks on interior frames and is lightest at the clip boundaries; the per-frame temporal-consistency gain (bars) follows the same shape.

Guidance	NFE	VBench $\uparrow$	UCF FVD $\downarrow$	Over- sat. $\downarrow$
CFG (fixed) [ 10 ]	50	84.0	380	0.21
APG [ 33 ]	50	84.1	377	0.14
$\beta$ -CFG [ 22 ]	50	84.2	375	0.15
CFG-Zero ⋆ [ 6 ]	50	84.3	372	0.13
AGAVE	1	85.2	372	0.10

Table 3: One step vs. multi-step adaptive CFG (14B). AGAVE at 1-NFE matches or beats adaptive guidance run on the 50-step teacher, with the lowest over-saturation (lower is better).

Figure 7: FVD–CLIP-T trade-off (UCF-101, 14B). At a single evaluation AGAVE lies beyond the front traced by the multi-step teacher and rCM, the empirical face of Prop. 1 .

Figure 8: Test-time controllability. Sweeping the scale

\omega_{\max}

, the AGAVE field (amber) dominates the iMF scalar (blue) over the entire FVD–CLIP-T curve, so the field is strictly more controllable.

Figure 9: Qualitative comparison. Rows are methods, columns are boundary and interior frames of one clip, with magnified insets. AGAVE removes the saturated highlights of scalar guidance on static regions and sharpens fast-moving foreground, while keeping more diverse boundary frames. More results are in Appendix E.

Configuration	VBench $\uparrow$	UCF FVD $\downarrow$	CLIP-T $\uparrow$
constant $\omega$ (= iMF)	83.0	464	0.298
+ step gate (CFG-Zero ⋆ )	84.2	428	0.300
+ linear ramp	84.2	419	0.301
+ Beta (fixed)	84.7	414	0.301
+ Beta (learned) = I 2 - CFG	84.9	391	0.305
+ motion-saliency	85.1	380	0.307

Table 4: Ablation (14B). Each axis helps; the interval-integrated schedule is dominant. A deliberately inverted (early-strong) schedule hurts , confirming the gain is a property of the correct field, not of added capacity.

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TrajCFG: Token-Wise Classifier-Free Guidance via Denoising Trajectory Feedback

Jingyu Liu, Hao Jiang, Yikang Ding, Huafeng Shi+5

Renmin University of China · Kling Team, Kuaishou Technology

Classifier-Free Guidance Diffusion Sampling Video Diffusion Models Flow Matching

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Classifier-free guidance (CFG) typically applies a shared scale to all latent tokens, although their velocity predictions evolve differently during sampling. We introduce Trajectory-Adaptive Classifier-Free Guidance (TrajCFG), a training-free method for flow-matching models that adapts token-wise guidance using historical changes in guided velocity direction. TrajCFG maps this feedback to bounded scales, assigning stronger guidance to larger directional changes and weaker guidance to more consistent directions. It combines adjacent-step and interval-normalized longer-span feedback, reusing standard CFG predictions without additional model evaluations. Controlled diagnostics and ablations examine the roles of directional feedback, token-wise allocation, and history-span fusion. Experiments on text-to-video, image-to-video, text-to-audio-video, text-to-image, and image-to-3D generation show improvements over base samplers across multiple backbones. For text-to-video generation, TrajCFG improves VBench Total scores by 0.30-0.75 points over the strongest evaluated baseline on each of three backbones. These results support historical directional feedback as a broadly applicable signal for fine-grained guidance allocation. The project page is available at https://jyliu-98.github.io/trajcfg-project-page/.

Abstract

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