Friction-Augmented Drifting Models for Resource-Efficient Domain Translation

Single-step generators promise high-fidelity synthesis at a fraction of the inference and training cost of ordinary differential equation (ODE)-based flow models, a central concern when compute is limited. Drifting Models (DMs) train a one-step generator by evolving samples under a kernel-based drift field, avoiding ODE integration entirely, but a two-particle surrogate of their iteration admits a locally repulsive regime in which repulsion can dominate the attraction to the target. We introduce DMF (Drifting Model with Friction), which scales the drift field by a linearly-scheduled coefficient 1-γ(i). A closed-form analysis of the surrogate gives a per-step contraction threshold and a finite-horizon bound on the error trajectory, suggesting why friction can halt the iteration before it relaxes to a spurious force-balance fixed point. On FFHQ latent-space domain translation, DMF significantly improves on the frictionless DM it extends in both Fréchet Inception Distance (FID; paired p=0.019, Cohen's d=1.71) and CLIP-MMD (CMMD; p=0.005, d=2.55) with no additional forward passes or parameters, and on a 2D task it sharply improves DM's Fréchet (moment-matching) error while remaining on par under the 2-Wasserstein distance. DMF also achieves FID and CMMD comparable to the far more expensive Optimal Flow Matching (OFM) in our runs, at roughly 29\times lower training wall-clock on identical hardware. DMF thus delivers these gains with a single scheduled scalar.