{"ID":2832415,"CreatedAt":"2026-06-01T04:54:23.091178241Z","UpdatedAt":"2026-06-01T04:54:23.091178241Z","DeletedAt":null,"paper_url":"https://arxiv.org/abs/2512.11858","arxiv_id":"2512.11858","title":"Adaptive Path Integral Diffusion: AdaPID","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.","short_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-v...","url_abs":"https://arxiv.org/abs/2512.11858","url_pdf":"https://arxiv.org/pdf/2512.11858v1","authors":"[\"Michael Chertkov\",\"Hamidreza Behjoo\"]","published":"2025-12-05T04:57:00Z","proceeding":"cs.LG","tasks":"[\"cs.LG\",\"cond-mat.stat-mech\",\"cs.AI\",\"eess.SY\",\"stat.ML\"]","methods":"[\"Diffusion Model\"]","has_code":false}