English

Adaptive Path Integral Diffusion: AdaPID

Machine Learning 2025-12-16 v1 Statistical Mechanics Artificial Intelligence Systems and Control Systems and Control Machine Learning

Abstract

Diffusion-based samplers -- Score Based Diffusions, Bridge Diffusions and Path Integral Diffusions -- match a target at terminal time, but the real leverage comes from choosing the schedule that governs the intermediate-time dynamics. We develop a path-wise schedule -- selection gramework for Harmonic PID with a time-varying stiffness, exploiting Piece-Wise-Constant(PWC) parametrizations and a simple hierarchical refinement. We introduce schedule-sensitive Quality-of-Sampling (QoS) diagnostics. Assuming a Gaussian-Mixture (GM) target, we retain closed-form Green functions' ration and numerically stable, Neural-Network free oracles for predicted-state maps and score. Experiments in 2D show that QoS driven PWC schedules consistently improve early-exit fidelity, tail accuracy, conditioning of the dynamics, and speciation (label-selection) timing at fixed integration budgets.

Keywords

Cite

@article{arxiv.2512.11858,
  title  = {Adaptive Path Integral Diffusion: AdaPID},
  author = {Michael Chertkov and Hamidreza Behjoo},
  journal= {arXiv preprint arXiv:2512.11858},
  year   = {2025}
}

Comments

51 pages, 17 figures

R2 v1 2026-07-01T08:22:40.370Z