{"ID":6537544,"CreatedAt":"2026-07-14T02:54:43.516908796Z","UpdatedAt":"2026-07-15T03:28:55.185153975Z","DeletedAt":null,"paper_url":"https://arxiv.org/abs/2607.11442","arxiv_id":"2607.11442","title":"Velocity Scheduled Flow Matching","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.","short_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 r...","url_abs":"https://arxiv.org/abs/2607.11442","url_pdf":"https://arxiv.org/pdf/2607.11442v1","authors":"[\"Vitalii Bondar\"]","published":"2026-07-13T11:50:06Z","proceeding":"cs.LG","tasks":"[\"cs.LG\"]","methods":"[]","has_code":false}