P3: Persistent Particle Planning for Constrained Diffusion Control

2026-10-05

AI Summary

This study addresses the challenge of simultaneously maintaining trajectory feasibility and consistency during test-time adaptation of diffusion models by proposing a persistent particle planning framework. The method unifies denoising and replanning as a Feynman–Kac particle system, optimizing control decisions through a maintained population of candidate plans combined with partial renoising and constraint-aware sampling. We theoretically demonstrate that preserving rare paths is more efficient and stable than sampling from scratch. Experiments show that the proposed framework effectively reduces route switching and constraint violations while decreasing the required number of iterations, achieving faster convergence and higher success rates in maze navigation tasks.

Abstract

Diffusion models provide expressive priors over trajectories, but adapting these priors to test-time constraints requires maintaining feasibility and consistency across successive control decisions. We introduce Persistent Particle Planning (P3), a sequential Monte Carlo framework for diffusion control that maintains a weighted population of candidate plans across replanning steps. At each control step, P3 shifts and partially re-noises the candidate trajectories, refines them under the latest observation, and uses constraint-aware weighting and resampling to select among alternative continuations without retraining the diffusion model. We consider denoising and replanning as one Feynman--Kac particle system and analyze it under an idealized repair. We prove that the re-noising depth controls how reliably a kept plan stays on its route, and that keeping a rare, well-separated route takes far fewer plans than rediscovering it by sampling from scratch. Experiments under multiple test-time constraint configurations show that population reuse reduces route switching and improves success without constraint violations. Because P3 refines earlier plans instead of redrawing them, it also needs fewer denoising iterations per replan. On maze-navigation tasks, it plans faster than both regenerated populations and methods that correct a single sampled plan by constrained optimization. Code and pretrained models are available at https://github.com/p3-username/p3-anon.

Problem

• Diffusion models
• Constrained control
• Trajectory planning
• Test-time constraints
• Consistency

Innovation

• Persistent Particle Planning
• Sequential Monte Carlo
• Diffusion Control
• Feynman-Kac Particle System
• Test-time Constraints