Improving Function Space Flow Matching with Kernel Optimal Transport

arXiv:2609.38049 · cs.LG · Submitted 2026-09-29 · Read on arXiv

cs.LG

Submitted: 2026-09-29

Updated: 2026-09-29

Code: https://github.com/heraclixus/KFFM

Project page: https://pythonot.github.io/40

Terminology

• Flow Matching — 1× in this paper · explained in 10 episodes
• Optimal Transport — 1× in this paper · explained in 5 episodes

Sources

• Lecture notes on rough paths and applications to machine learning
• Analysis and Probability on Infinite-Dimensional Spaces
• Minibatch optimal transport distances; analysis and applications
• Operator Flow Matching for Timeseries Forecasting
• pySigLib -- Fast Signature-Based Computations on CPU and GPU
• OAT-FM: Optimal Acceleration Transport for Improved Flow Matching
• Gaussian Optimal Transport Beyond Brenier's Theorem
• Flow Straight and Fast in Hilbert Space: Functional Rectified Flow
• Characteristic kernels on Hilbert spaces, Banach spaces, and on sets of measures

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