arXiv Machine Learning
Transport along Local Annealing Paths: Wasserstein Geometry and Multimodal Sampling
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arXiv Machine Learning
Jun 30
The Fundamental Limits of Valid Transport Map Estimation
arXiv:2606. 30574v1 Announce Type: new Abstract: Many modern generative modeling methods, including diffusion models, normalizing flows, and flow matching, estimate transport maps or plans between distributions without explicitly targeting an optimal transport (OT) map.
Hugging Face Trending Papers
Jun 29
The Fundamental Limits of Valid Transport Map Estimation
Many modern generative modeling methods, including diffusion models, normalizing flows, and flow matching, estimate transport maps or plans between distributions without explicitly targeting an optimal transport (OT) map. In applications like generative modeling, the transport cost itself is irrelevant, and this makes it natural to target maps which are more tractable from either a statistical or computational standpoint.
arXiv Statistics ML
Oct 2
Wasserstein Gradient Flows and Forward-Only Diffusion Are Not Enough for Multimodal Sampling
arXiv:2610.02081v1 Announce Type: new Abstract: There has been a proliferation of sampling algorithms based on Wasserstein gradient flows (WGF) and forward-only diffusion processes (FODP), often acco...
arXiv Statistics ML
Sep 10
Manifold-Aligned Generative Transport
arXiv:2602.19600v2 Announce Type: replace Abstract: Many high-dimensional datasets concentrate near a low-dimensional structure embedded in the ambient space. Generative models for such data must con...
arXiv AI
Oct 2
Discrete Wasserstein Flows for One-Step Generative Modeling
The paper presents a new one‑step generative modeling framework for finite state spaces, leveraging discrete Wasserstein geometry to define a target‑relative KL gradient flow over a reversible Markov kernel. The authors implement this flow at the particle level using Markov jumps and encode the resulting transport updates into a latent‑conditioned generator, enabling one‑step inference after training. Experiments on a controlled setting confirm KL dissipation, consistency between particle dynamics and probability flow, and accurate numerical scaling, while a finite‑capacity neural generator successfully tracks the exact transport targets.
arXiv Machine Learning
Jun 2
A Biconvex Formulation for Stable Transport of Mixture Models with a Unique Solution
arXiv:2606. 02515v1 Announce Type: new Abstract: Optimal transport (OT) provides a principled framework for mapping between probability distributions.