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

2026-04-20

AI Summary

This work addresses two fundamental issues in conventional drift models: the presence of local repulsion during iterative drift field updates and whether vanishing drift alone suffices to guarantee alignment between the learned and target distributions. To resolve these, the authors propose Drift Models with Friction (DMF), which introduces a linearly scheduled friction coefficient to guide sample evolution via kernel-driven drift fields within a generative framework that avoids ODE integration. They establish identifiability theory for drift field equilibria and, specifically under Gaussian kernels, prove that vanishing drift uniquely determines the target distribution, providing associated error bounds and contraction thresholds. Experiments demonstrate that on the FFHQ adult-to-child domain translation task, DMF achieves or surpasses the performance of Optimal Flow Matching with 16× less training computation.

Technology Category

• Computer Vision: Diffusion Models for Vision
• Machine Learning: Learning with Manifolds
• Search and Optimization: Learning to Search

Application Category

• Graph Algorithms and Modeling for the Web: Foundation models and LLMs for Web-related graphs
• User Modeling, Personalization and Recommendation: Fairness-aware retrieval and ranking
• Search and Retrieval-Augmented AI: Web learning to rank, online learning, and counterfactual learning for ranking

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.

Problem

• Drifting Models
• drift field
• distribution matching
• repulsive regime
• equilibrium identifiability

Innovation

• Drifting Model
• Friction-Augmented Dynamics
• Contraction Threshold
• Equilibrium Identifiability
• Flow Matching