Local Fokker--Planck Geometry for Score Estimation: Heat-Ball Mean-Value Representations and Exact High-Dimensional Sampling

arXiv:2606.27954 · stat.ML, math.AP · Submitted 2026-06-26 · Read on arXiv

Jiayao Bai, Lang Deng, Yi Du, Yifei Jia

stat.ML, math.AP

Submitted: 2026-06-26

Comments: 24 pages, 11 figures, 5 tables

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

Terminology

• Monotonicity — 10× in this paper · explained in 2 episodes
• Accuracy — 6× in this paper · explained in 1 episode
• Generative Model — 6× in this paper · explained in 2 episodes
• Generative Models — 6× in this paper · explained in 3 episodes
• Generative Modeling — 5× in this paper · explained in 3 episodes
• Generalization — 4× in this paper · explained in 14 episodes
• Core — 3× in this paper · explained in 2 episodes
• Robustness — 3× in this paper · explained in 6 episodes
• Score Function — 3× in this paper · explained in 4 episodes
• Verification — 3× in this paper · explained in 2 episodes
• Flow Matching — 2× in this paper · explained in 22 episodes
• Adam — 1× in this paper · explained in 3 episodes
• Benchmark — 1× in this paper · explained in 2 episodes
• Degeneracy — 1× in this paper · explained in 4 episodes
• Denoising Autoencoder — 1× in this paper · explained in 2 episodes
• Diffusion Model — 1× in this paper · explained in 10 episodes
• Diffusion Models — 1× in this paper · explained in 9 episodes
• Effective Sample Size (ESS) — 1× in this paper · explained in 2 episodes
• Fidelity — 1× in this paper · explained in 2 episodes
• Gradient Flow — 1× in this paper · explained in 2 episodes
• Hyperparameters — 1× in this paper · explained in 2 episodes
• Inflation — 1× in this paper · explained in 2 episodes
• Initial Data — 1× in this paper · explained in 2 episodes
• Normalizing Flow — 1× in this paper · explained in 4 episodes
• Normalizing Flows — 1× in this paper · explained in 4 episodes
• PDE residual — 1× in this paper · explained in 2 episodes
• Parameterization — 1× in this paper · explained in 2 episodes
• Reconstruction Error — 1× in this paper · explained in 2 episodes
• Training Objective — 1× in this paper · explained in 3 episodes

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