# On the Wasserstein Gradient Flow Interpretation of Drifting Models

arXiv: https://arxiv.org/abs/2605.05118 · HTML: https://mlsanity.com/paper/2605.05118/

## Key facts

- Cited by 11 papers in the map (data through 14 Oct 2026).
- Builds on 21 of its 31 references that are in the map.
- First posted on arXiv 6 May 2026.

## Builds on (most cited first, 21 of 21)

- [Sinkhorn Distances: Lightspeed Computation of Optimal Transportation Distances](https://mlsanity.com/paper/1306.0895/) (2013)
- [f-GAN: Training Generative Neural Samplers using Variational Divergence Minimization](https://mlsanity.com/paper/1606.00709/) (2016)
- [Generative Moment Matching Networks](https://mlsanity.com/paper/1502.02761/) (2015)
- [On Wasserstein Two Sample Testing and Related Families of Nonparametric Tests](https://mlsanity.com/paper/1509.02237/) (2015)
- [Training generative neural networks via Maximum Mean Discrepancy optimization](https://mlsanity.com/paper/1505.03906/) (2015)
- [Maximum Mean Discrepancy Gradient Flow](https://mlsanity.com/paper/1906.04370/) (2019)
- [Generative Modeling via Drifting](https://mlsanity.com/paper/2602.04770/) (2026)
- [Inductive Moment Matching](https://mlsanity.com/paper/2503.07565/) (2025)
- [Sliced-Wasserstein Flows: Nonparametric Generative Modeling via Optimal Transport and Diffusions](https://mlsanity.com/paper/1806.08141/) (2018)
- [KALE Flow: A Relaxed KL Gradient Flow for Probabilities with Disjoint Support](https://mlsanity.com/paper/2106.08929/) (2021)
- [Blindness of score-based methods to isolated components and mixing proportions](https://mlsanity.com/paper/2008.10087/) (2020)
- [Sinkhorn-Drifting Generative Models](https://mlsanity.com/paper/2603.12366/) (2026)
- [Generative Drifting is Secretly Score Matching: a Spectral and Variational Perspective](https://mlsanity.com/paper/2603.09936/) (2026)
- [Deep MMD Gradient Flow without adversarial training](https://mlsanity.com/paper/2405.06780/) (2024)
- [Gradient Flow Drifting: Generative Modeling via Wasserstein Gradient Flows of KDE-Approximated Divergences](https://mlsanity.com/paper/2603.10592/) (2026)
- [(De)-regularized Maximum Mean Discrepancy Gradient Flow](https://mlsanity.com/paper/2409.14980/) (2024)
- [Drifting Fields are not Conservative](https://mlsanity.com/paper/2604.06333/) (2026)
- [A Long-Short Flow-Map Perspective for Drifting Models](https://mlsanity.com/paper/2602.20463/) (2026)
- [The Score-Difference Flow for Implicit Generative Modeling](https://mlsanity.com/paper/2304.12906/) (2023)
- [Long-Time Asymptotics of the Sliced-Wasserstein Flow](https://mlsanity.com/paper/2405.06313/) (2024)
- [Solving Fredholm Integral Equations of the First Kind via Wasserstein Gradient Flows](https://mlsanity.com/paper/2209.09936/) (2022)

## Built on by (most cited first, 11 of 11)

- [Finite-Particle Convergence Rates for Conservative and Non-Conservative Drifting Models](https://mlsanity.com/paper/2605.22795/) (2026)
- [Uniform-in-time Propagation-of-Chaos for Stein Variational Gradient Descent](https://mlsanity.com/paper/2607.00149/) (2026)
- [Wasserstein gradient flows for Coulomb discrepancies](https://mlsanity.com/paper/2607.12579/) (2026)
- [A Gradient Flow Perspective on Minimum MMD Estimation](https://mlsanity.com/paper/2607.03871/) (2026)
- [Finite-Probe Total-Variation Certificates for Finite-Basis Drifting Models](https://mlsanity.com/paper/2608.01547/) (2026)
- [Refresh or Realize? Compute Allocation in Drifting Models](https://mlsanity.com/paper/2609.32298/) (2026)
- [One-Step Generative Modeling via Unbalanced Optimal Transport](https://mlsanity.com/paper/2609.32708/) (2026)
- [One-Step Generation via Riemannian Wasserstein Gradient Flows](https://mlsanity.com/paper/2610.04454/) (2026)
- [Learning Discriminative Geometry for Drifting Models](https://mlsanity.com/paper/2610.04703/) (2026)
- [Amortised Inference through One-Step Implicit Sampling](https://mlsanity.com/paper/2610.12679/) (2026)
- [Drift, Then Spread: Learning One-Step Generative Policies for Online Reinforcement Learning](https://mlsanity.com/paper/2610.15662/) (2026)

## Abstract (arXiv)

Recently, Deng et al. (2026) proposed Generative Modeling via Drifting (GMD), a novel framework for generative tasks. This note presents an analysis of GMD through the lens of Wasserstein Gradient Flows (WGF), i.e., the path of steepest descent for a functional in the space of probability measures, equipped with the geometry of optimal transport. Unlike previous WGF-based contributions, GMD can be thought of as directly targeting a fixed point of a specific WGF flow. We demonstrate three main results: first, that one algorithm proposed by Deng et al. (2026) corresponds to finding the limiting point of a WGF on the KL divergence, with Parzen smoothing on the densities. Second, that the algorithm actually implemented by Deng et al. (2026) corresponds to a different procedure, which bears some resemblance to the fixed point of a WGF on the Sinkhorn divergence, but lacks certain desirable properties of the latter. Third, the same same idea can be extended to the limiting point of other WGFs, including the Maximum Mean Discrepancy (MMD), the sliced Wasserstein distance, and GAN critic functions.