On the Wasserstein Gradient Flow Interpretation of Drifting Models
Arthur Gretton, Li Kevin Wenliang, Alexandre Galashov, James Thornton, Valentin De Bortoli + 1 more
TLDR
This paper analyzes Generative Modeling via Drifting (GMD) through Wasserstein Gradient Flows, revealing its connection to fixed points of WGFs.
Key contributions
- GMD targets a fixed point of a specific Wasserstein Gradient Flow (WGF).
- One GMD algorithm corresponds to a WGF on KL divergence with Parzen smoothing.
- The implemented GMD algorithm resembles a WGF on Sinkhorn divergence but has limitations.
- The WGF fixed-point idea extends to MMD, sliced Wasserstein, and GAN critics.
Why it matters
This work provides a crucial theoretical understanding of GMD, a new generative framework. By interpreting GMD through WGFs, it clarifies its underlying mechanics and opens avenues for extending its application to other divergences. This deepens our understanding of generative models.
Original Abstract
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.
📬 Weekly AI Paper Digest
Get the top 10 AI/ML arXiv papers from the week — summarized, scored, and delivered to your inbox every Monday.