提出自适应路径积分扩散，提升采样精度与效率。
Adaptive Path Integral Diffusion: AdaPID
- 用分段常数参数化设计动态调节的路径调度策略。
- 在2D实验中显著改善早期退出精度、尾部概率和标签选择时机。
- 无需神经网络，基于高斯混合目标实现稳定且可解析的采样器。
基于扩散的采样器——基于得分的扩散、桥接扩散与路径积分扩散——在终时刻匹配目标分布，但其真正优势在于中间时间动态的调度选择。本文为谐波路径积分扩散（Harmonic PID）设计了一种路径级调度选择框架，采用分段常数（PWC）参数化并结合简单层级优化。引入对调度敏感的采样质量诊断（QoS）。假设目标为高斯混合模型（GM），保留闭式格林函数比值，并构建无神经网络、数值稳定的预测状态映射与得分计算工具。2D实验表明，在固定积分预算下，基于QoS驱动的PWC调度能持续提升早期退出保真度、尾部概率准确性、动力学条件性以及标签选择（speciation）时机。
原文摘要 · Abstract (English)
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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