# Friction-Augmented Drifting Models for Resource-Efficient Domain Translation

arXiv: https://arxiv.org/abs/2604.18194 · HTML: https://mlsanity.com/paper/2604.18194/

## Key facts

- Cited by 3 papers in the map (data through 14 Oct 2026).
- Builds on 15 of its 19 references that are in the map.
- First posted on arXiv 20 Apr 2026.

## Builds on (most cited first, 15 of 15)

- [Score-Based Generative Modeling through Stochastic Differential Equations](https://mlsanity.com/paper/2011.13456/) (2020)
- [A Style-Based Generator Architecture for Generative Adversarial Networks](https://mlsanity.com/paper/1812.04948/) (2018)
- [Flow Matching for Generative Modeling](https://mlsanity.com/paper/2210.02747/) (2022)
- [Flow Straight and Fast: Learning to Generate and Transfer Data with Rectified Flow](https://mlsanity.com/paper/2209.03003/) (2022)
- [Building Normalizing Flows with Stochastic Interpolants](https://mlsanity.com/paper/2209.15571/) (2022)
- [Improving and generalizing flow-based generative models with minibatch optimal transport](https://mlsanity.com/paper/2302.00482/) (2023)
- [Input Convex Neural Networks](https://mlsanity.com/paper/1609.07152/) (2016)
- [Rethinking FID: Towards a Better Evaluation Metric for Image Generation](https://mlsanity.com/paper/2401.09603/) (2023)
- [Optimal transport mapping via input convex neural networks](https://mlsanity.com/paper/1908.10962/) (2019)
- [Adversarial Latent Autoencoders](https://mlsanity.com/paper/2004.04467/) (2020)
- [Neural Optimal Transport](https://mlsanity.com/paper/2201.12220/) (2022)
- [Generative Modeling via Drifting](https://mlsanity.com/paper/2602.04770/) (2026)
- [Do Neural Optimal Transport Solvers Work? A Continuous Wasserstein-2 Benchmark](https://mlsanity.com/paper/2106.01954/) (2021)
- [Optimal Flow Matching: Learning Straight Trajectories in Just One Step](https://mlsanity.com/paper/2403.13117/) (2024)
- [Sinkhorn-Drifting Generative Models](https://mlsanity.com/paper/2603.12366/) (2026)

## Built on by (most cited first, 3 of 3)

- [DriftXpress: Faster Drifting Models via Projected RKHS Fields](https://mlsanity.com/paper/2605.12183/) (2026)
- [Second Order Drifting Models](https://mlsanity.com/paper/2608.07924/) (2026)
- [Identifiability and Stability of Generative Drifting in the Companion-Elliptic Kernel Family](https://mlsanity.com/paper/2604.24196/) (2026)

## Abstract (arXiv)

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 Fr'echet 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 Fr'echet (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× lower training wall-clock on identical hardware. DMF thus delivers these gains with a single scheduled scalar.