Velocity Scheduled Flow Matching

• URL: http://arxiv.org/abs/2607.11442v1
• Date: Mon, 13 Jul 2026 11:50:06 GMT
• Title: Velocity Scheduled Flow Matching
• Abstract summary: Flow matching trains a neural network to regress the conditional velocity along a linear interpolant between noise and data.<n>We introduce Velocity Scheduled Flow Matching, which replaces the conditional target.<n>VSFM can be sampled under any admissible profile by integrating its ODE on a non-uniform profile.
• Score: 0.0
• License: http://creativecommons.org/licenses/by/4.0/
• Abstract: Flow matching trains a neural network to regress the conditional velocity along a linear interpolant between noise and data, and the number of network evaluations~(NFE) sets the cost of sampling. The straight-line interpolant carries an implicit choice: the sample moves at constant speed throughout the trajectory. We relax this choice and introduce Velocity Scheduled Flow Matching~(VSFM), which replaces the conditional target $x_1 - x_0$ with $v(t)(x_1 - x_0)$ for any nonnegative profile $v:[0,1]\to\mathbb{R}_{\geq 0}$ satisfying $\int_0^1 v\,dt = 1$. We study six polynomial profiles drawn from motion planning. The first use of VSFM is at inference time: a pretrained linear flow-matching model can be sampled under any admissible profile by integrating its ODE on a non-uniform $τ$-schedule, with no retraining and no additional computation; on CIFAR-10 this lowers FID by up to $19.8\%$. Training from scratch under a braking profile gives a further reduction of $17.4\%$ at $4$~NFE. Both gains follow from the local truncation error of the Euler integrator on the induced grid.

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