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

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.