Attraction, Repulsion, and Friction: Introducing DMF, a Friction-Augmented Drifting Model
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arXiv
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| Autores principales: | , , , , |
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| Formato: | Preprint |
| Publicado: |
2026
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| _version_ | 1866910148594761728 |
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| author | Kazanskii, Arkadii Petrova, Tatiana Bagrianskii, Konstantin Puzikov, Aleksandr State, Radu |
| author_facet | Kazanskii, Arkadii Petrova, Tatiana Bagrianskii, Konstantin Puzikov, Aleksandr State, Radu |
| contents | 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. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2604_18194 |
| institution | arXiv |
| publishDate | 2026 |
| record_format | arxiv |
| spellingShingle | Attraction, Repulsion, and Friction: Introducing DMF, a Friction-Augmented Drifting Model Kazanskii, Arkadii Petrova, Tatiana Bagrianskii, Konstantin Puzikov, Aleksandr State, Radu Machine Learning Computer Vision and Pattern Recognition I.2.6; G.3 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. |
| title | Attraction, Repulsion, and Friction: Introducing DMF, a Friction-Augmented Drifting Model |
| topic | Machine Learning Computer Vision and Pattern Recognition I.2.6; G.3 |
| url | https://arxiv.org/abs/2604.18194 |