# Gradient Flow Drifting: Generative Modeling via Wasserstein Gradient Flows of KDE-Approximated Divergences

arXiv: https://arxiv.org/abs/2603.10592 · HTML: https://mlsanity.com/paper/2603.10592/

## Key facts

- Cited by 17 papers in the map (data through 14 Oct 2026).
- Builds on 11 of its 17 references that are in the map.
- First posted on arXiv 11 Mar 2026.

## Builds on (most cited first, 11 of 11)

- [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)
- [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)
- [Scalable Wasserstein Gradient Flow for Generative Modeling through Unbalanced Optimal Transport](https://mlsanity.com/paper/2402.05443/) (2024)
- [MonoFlow: Rethinking Divergence GANs via the Perspective of Wasserstein Gradient Flows](https://mlsanity.com/paper/2302.01075/) (2023)
- [Weighted quantization using MMD: From mean field to mean shift via gradient flows](https://mlsanity.com/paper/2502.10600/) (2025)
- [A Long-Short Flow-Map Perspective for Drifting Models](https://mlsanity.com/paper/2602.20463/) (2026)
- [Quantitative Convergence of Wasserstein Gradient Flows of Kernel Mean Discrepancies](https://mlsanity.com/paper/2603.01977/) (2026)

## Built on by (most cited first, 17 of 17)

- [One-Step Generative Modeling via Wasserstein Gradient Flows](https://mlsanity.com/paper/2605.11755/) (2026)
- [Drifting Fields are not Conservative](https://mlsanity.com/paper/2604.06333/) (2026)
- [On the Wasserstein Gradient Flow Interpretation of Drifting Models](https://mlsanity.com/paper/2605.05118/) (2026)
- [Kernel-Gradient Drifting Models](https://mlsanity.com/paper/2605.10727/) (2026)
- [Finite-Particle Convergence Rates for Conservative and Non-Conservative Drifting Models](https://mlsanity.com/paper/2605.22795/) (2026)
- [Drifting Field Policy: A One-Step Generative Policy via Wasserstein Gradient Flow](https://mlsanity.com/paper/2605.07727/) (2026)
- [DriftXpress: Faster Drifting Models via Projected RKHS Fields](https://mlsanity.com/paper/2605.12183/) (2026)
- [Uniform-in-time Propagation-of-Chaos for Stein Variational Gradient Descent](https://mlsanity.com/paper/2607.00149/) (2026)
- [Analytical Correction for Subsampling Bias in Drifting Models](https://mlsanity.com/paper/2604.27239/) (2026)
- [Second Order Drifting Models](https://mlsanity.com/paper/2608.07924/) (2026)
- [Unifying Distributional Training for One-Step Visual Generation](https://mlsanity.com/paper/2609.35763/) (2026)
- [Identifiability and Stability of Generative Drifting in the Companion-Elliptic Kernel Family](https://mlsanity.com/paper/2604.24196/) (2026)
- [Difference of Convex Programming in the Wasserstein Space with Applications to MMD Optimization](https://mlsanity.com/paper/2606.27767/) (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)

## Abstract (arXiv)

We reveal a precise mathematical framework about a new family of generative models which we call Gradient Flow Drifting. With this framework, we prove an equivalence between the recently proposed Drifting Model and the Wasserstein gradient flow of the forward KL divergence under kernel density estimation (KDE) approximation. Specifically, we prove that the drifting field of drifting model (arXiv:2602.04770) equals, up to a bandwidth-squared scaling factor, the difference of KDE log-density gradients nabla log pkde - nabla log qkde, which is exactly the particle velocity field of the Wasserstein-2 gradient flow of KL(q|p) with KDE-approximated densities. Besides that, this broad family of generative models can also include MMD-based generators, which arises as special cases of Wasserstein gradient flows of different divergences under KDE approximation. We provide a concise identifiability proof, and a theoretically grounded mixed-divergence strategy. We combine reverse KL and chi2 divergence gradient flows to simultaneously avoid mode collapse and mode blurring, and extend this method onto Riemannian manifold which loosens the constraints on the kernel function, and makes this method more suitable for the semantic space. Preliminary experiments on synthetic benchmarks validate the framework.