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

TL;DR

The paper introduces DMF, a friction-augmented drifting model that improves generative modeling efficiency and accuracy, addressing open questions about drift-field behavior and distribution matching.

Contribution

It derives a contraction threshold for the surrogate, proves equilibrium identifiability under Gaussian kernels, and demonstrates DMF's superior performance with lower training compute.

Findings

DMF matches or exceeds Optimal Flow Matching on FFHQ domain translation.

A linearly-scheduled friction coefficient bounds error trajectories.

Vanishing drift implies distribution equality under Gaussian kernels.

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.