Attraction, Repulsion, and Friction: Introducing DMF, a Friction-Augmented Drifting Model

• URL: http://arxiv.org/abs/2604.18194v1
• Date: Mon, 20 Apr 2026 12:47:27 GMT
• Title: Attraction, Repulsion, and Friction: Introducing DMF, a Friction-Augmented Drifting Model
• Abstract summary: We show that a linearly-scheduled friction gives a finite-horizon bound on the error trajectory.<n>Our friction-augmented model, DMF, matches or exceeds Optimal Flow Matching on FFHQ coefficient adult-to-child domain translation.
• Score: 37.847379736905175
• License: http://creativecommons.org/licenses/by/4.0/
• Abstract: Drifting Models [Deng et al., 2026] train a one-step generator by evolving samples under a kernel-based drift field, avoiding ODE integration at inference. The original analysis leaves two questions open. The drift-field iteration admits a locally repulsive regime in a two-particle surrogate, and vanishing of the drift ($V_{p,q}\equiv 0$) is not known to force the learned distribution $q$ to match the target $p$. We derive a contraction threshold for the surrogate and show that a linearly-scheduled friction coefficient gives a finite-horizon bound on the error trajectory. Under a Gaussian kernel we prove that the drift-field equilibrium is identifiable: vanishing of $V_{p,q}$ on any open set forces $q=p$, closing the converse of Proposition 3.1 of Deng et al. Our friction-augmented model, DMF (Drifting Model with Friction), matches or exceeds Optimal Flow Matching on FFHQ adult-to-child domain translation at 16x lower training compute.

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