Adaptive Path Integral Diffusion: AdaPID
This work addresses a specific bottleneck in diffusion sampling for computational statistics, offering incremental improvements in schedule optimization.
The paper tackles the problem of improving diffusion-based samplers by adaptively selecting schedules for intermediate-time dynamics, resulting in enhanced early-exit fidelity, tail accuracy, conditioning, and speciation timing in 2D experiments with Gaussian-Mixture targets.
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.