2025/12/05 by Chertkov, Michael, Behjoo, Hamidreza
#Artificial Intelligence (cs.AI) #FOS: Computer and information sciences #FOS: Electrical engineering #FOS: Physical sciences #Machine Learning (cs.LG) #Machine Learning (stat.ML) #Statistical Mechanics (cond-mat.stat-mech) #Systems and Control (eess.SY) #electronic engineering #information engineering
paper · doi:10.48550/arxiv.2512.11858
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.