Discretization and Statistical Consistency of Functional Flow Matching

arXiv:2608.04531 · cs.LG, math.PR, stat.ML · Submitted 2026-08-05 · Read on arXiv

cs.LG, math.PR, stat.ML

Submitted: 2026-08-05

Updated: 2026-10-23

Comments: 31 pages, 2 tables

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

Terminology

• Flow Matching — 30× in this paper · explained in 22 episodes
• Consistency — 29× in this paper · explained in 3 episodes
• Hilbert Space — 7× in this paper · explained in 2 episodes
• Orthogonal Projection — 7× in this paper · explained in 2 episodes
• Trace — 7× in this paper · explained in 2 episodes
• Papers — 5× in this paper · explained in 3 episodes
• Adam — 3× in this paper · explained in 3 episodes
• DeepONet — 3× in this paper · explained in 2 episodes
• Neural Operators — 3× in this paper · explained in 2 episodes
• Rectified Flow — 3× in this paper · explained in 3 episodes
• Diffusion Model — 2× in this paper · explained in 10 episodes
• Diffusion Models — 2× in this paper · explained in 9 episodes
• Wasserstein Distance — 2× in this paper · explained in 6 episodes
• Accuracy — 1× in this paper · explained in 1 episode
• Benchmark — 1× in this paper · explained in 2 episodes
• Composition — 1× in this paper · explained in 2 episodes
• Editor — 1× in this paper · explained in 2 episodes
• Error Decomposition — 1× in this paper · explained in 4 episodes
• Fixed Point — 1× in this paper · explained in 2 episodes
• Generative Modeling — 1× in this paper · explained in 3 episodes
• Gradient Flow — 1× in this paper · explained in 2 episodes
• Localization — 1× in this paper · explained in 2 episodes
• Monotonicity — 1× in this paper · explained in 2 episodes
• Verification — 1× in this paper · explained in 2 episodes

Sources

• Scale-Adaptive Generative Flows for Multiscale Scientific Data
• Optimal-Transport-Guided Functional Flow Matching for Turbulent Field Generation in Hilbert Space
• Probability-Flow ODE in Infinite-Dimensional Function Spaces

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