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.
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: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: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...
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:2606. 02515v1 Announce Type: new Abstract: Optimal transport (OT) provides a principled framework for mapping between probability distributions.
Particle-based variational inference (ParVI) methods approximate an intractable target distribution by evolving an ensemble of interacting samples. Existing approaches rely predominantly on kernel-based repulsion (e.
The paper introduces COFM, a framework for consistent optimal transport flow matching that uses partially input convex neural networks (PICNN) to parameterize the transport potential. By adding a Hamilton‑Jacobi residual to the training objective, COFM enforces dynamical consistency and supports both one‑step transport and multi‑step ODE sampling without costly inner optimization. Experiments on benchmark datasets show that COFM achieves competitive performance while reducing L^2‑UVP by over 2× and cutting computational time by about 9× compared to state‑of‑the‑art models.
arXiv:2605. 12174v2 Announce Type: replace Abstract: Solving optimal transport (OT) on random minibatches is a common surrogate for exact OT in large-scale learning.
arXiv:2606. 25265v1 Announce Type: new Abstract: Particle-based variational inference (ParVI) methods approximate an intractable target distribution by evolving an ensemble of interacting samples.
The paper introduces a new optimal transport framework that uses the Barron energy—an intrinsic neural network complexity measure—instead of the traditional kinetic energy. By modeling transport as deep residual networks that map a reference distribution to a target distribution, the authors define a new metric on probability measures and analyze its properties for generative modeling. They demonstrate that diffusion generative models are suboptimal in this Barron geometry and explore how adaptivity can improve alternative generative approaches.
arXiv:2601. 21026v2 Announce Type: replace-cross Abstract: Sampling configurations at thermodynamic equilibrium is a central challenge in statistical physics.