# A Long-Short Flow-Map Perspective for Drifting Models

arXiv: https://arxiv.org/abs/2602.20463 · HTML: https://mlsanity.com/paper/2602.20463/

## Key facts

- Cited by 10 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 24 Feb 2026.

## Built on by (most cited first, 10 of 10)

- [Generative Drifting is Secretly Score Matching: a Spectral and Variational Perspective](https://mlsanity.com/paper/2603.09936/) (2026)
- [Gradient Flow Drifting: Generative Modeling via Wasserstein Gradient Flows of KDE-Approximated Divergences](https://mlsanity.com/paper/2603.10592/) (2026)
- [A Unified View of Score-Based and Drifting Models](https://mlsanity.com/paper/2603.07514/) (2026)
- [On the Wasserstein Gradient Flow Interpretation of Drifting Models](https://mlsanity.com/paper/2605.05118/) (2026)
- [Finite-Particle Convergence Rates for Conservative and Non-Conservative Drifting Models](https://mlsanity.com/paper/2605.22795/) (2026)
- [Implicit Drifting Policy: One-Step Action Generation via Conditional Expert Geometry](https://mlsanity.com/paper/2606.01098/) (2026)
- [Second Order Drifting Models](https://mlsanity.com/paper/2608.07924/) (2026)
- [DriftST: One-Step Generative Inference of Spatial Transcriptomics from H&E Histology](https://mlsanity.com/paper/2607.04740/) (2026)
- [Refresh or Realize? Compute Allocation in Drifting Models](https://mlsanity.com/paper/2609.32298/) (2026)
- [Multi-Bandwidth Distribution Matching Distillation: On the Equivalence of Distribution Matching Distillation and Drifting Models](https://mlsanity.com/paper/2610.10989/) (2026)

## Abstract (arXiv)

This paper provides a reinterpretation of the Drifting Model~citedeng2026generative through a semigroup-consistent long-short flow-map factorization. We show that a global transport process can be decomposed into a long-horizon flow map followed by a short-time terminal flow map admitting a closed-form optimal velocity representation, and that taking the terminal interval length to zero recovers exactly the drifting field together with a conservative impulse term required for flow-map consistency. Based on this perspective, we propose a new likelihood learning formulation that aligns the long-short flow-map decomposition with density evolution under transport. We validate the framework through both theoretical analysis and empirical evaluations on benchmark tests, and further provide a theoretical interpretation of the feature-space optimization while highlighting several open problems for future study.