Adaptive Path Integral Diffusion: AdaPID

TL;DR

This paper introduces a novel adaptive scheduling framework for diffusion-based samplers, improving their efficiency and accuracy by optimizing intermediate dynamics using piece-wise constant parametrizations and QoS diagnostics.

Contribution

It develops a path-wise schedule selection framework for Harmonic PID with time-varying stiffness, incorporating QoS diagnostics and stable neural network-free oracles for target sampling.

Findings

QoS-driven schedules enhance early-exit fidelity

Improved tail accuracy and dynamics conditioning

Better label-selection timing at fixed budgets

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.