Adaptive Path Integral Diffusion: AdaPID

• URL: http://arxiv.org/abs/2512.11858v1
• Date: Fri, 05 Dec 2025 04:57:00 GMT
• Title: Adaptive Path Integral Diffusion: AdaPID
• Abstract summary: We develop a path-wise schedule for selection gramework for Harmonic PID with a time-varying stiffness.<n>We introduce schedule-sensitive Quality-of-Sampling (QoS) diagnostics.
• Score: 0.0
• License: http://creativecommons.org/licenses/by/4.0/
• 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.

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