Potential Matching Optimal Transport: Continuous Normalizing Flows for Exact p-Wasserstein Dynamics

arXiv:2608.05666 · cs.LG, math.NA · Submitted 2026-08-06 · Read on arXiv

Lishuo Zhang, Ruizhi Huang, Yang Yu, Lei Li

School of Mathematical Sciences, Shanghai Jiao Tong University · School of Mathematical Sciences, Shanghai Jiao Tong University · School of Mathematical Sciences, Shanghai Jiao Tong University · Institute of Natural Sciences, MOE-LSC, Shanghai Jiao Tong University

cs.LG, math.NA

Submitted: 2026-08-06

License: http://arxiv.org/licenses/nonexclusive-distrib/1.0/

Terminology

• Optimal Transport — 29× in this paper · explained in 5 episodes
• Potential Matching Optimal Transport — 6× in this paper
• Benchmark — 5× in this paper · explained in 2 episodes
• Distribution Matching — 5× in this paper · explained in 4 episodes
• Normalizing Flow — 5× in this paper · explained in 4 episodes
• Normalizing Flows — 4× in this paper · explained in 4 episodes
• Flow Matching — 3× in this paper · explained in 22 episodes
• Generative Model — 3× in this paper · explained in 2 episodes
• Generative Models — 3× in this paper · explained in 3 episodes
• Parameterization — 3× in this paper · explained in 2 episodes
• Generative Modeling — 2× in this paper · explained in 3 episodes
• Regularization — 2× in this paper · explained in 3 episodes
• Consistency — 1× in this paper · explained in 3 episodes
• Fidelity — 1× in this paper · explained in 2 episodes
• Optimal Transport (OT) — 1× in this paper · explained in 9 episodes
• Papers — 1× in this paper · explained in 3 episodes
• Sufficiency — 1× in this paper · explained in 2 episodes

Sources

• FFJORD: Free-form Continuous Dynamics for Scalable Reversible Generative Models
• Improving and generalizing flow-based generative models with minibatch optimal transport

Related papers

• Polynomial-Augmented Neural Networks (PANNs) with Weak Orthogonality Constraints for Enhanced Function and PDE Approximation
• AIRL-S: Unifying Reinforcement Learning and Search-Based Test-Time Scaling via Adversarial Inverse Reinforcement Learning
• Transformers as Bayesian In-Context Experimenters: Smoothness-Adaptive Efficient ATE Estimation
• Convergence issues in Relational Concept Analysis based on AOC-posets
• Beliefs Beyond Posteriors: The Predictive Cost of ELBO Binding
• Understanding Diffusion Models via Ratio-Based Function Approximation with SignReLU Networks