Attraction, Repulsion, and Friction: Introducing DMF, a Friction-Augmented Drifting Model
For researchers in generative modeling, this work provides theoretical guarantees and a practical improvement for Drifting Models, though it is incremental as it builds on an existing framework.
The authors address two open questions in Drifting Models: the lack of a contraction guarantee and the non-identifiability of the drift-field equilibrium. They prove a contraction threshold, show identifiability under a Gaussian kernel, and introduce DMF (Drifting Model with Friction) which matches or exceeds Optimal Flow Matching on FFHQ adult-to-child domain translation with 16x lower training compute.
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.