# P3: Persistent Particle Planning for Constrained Diffusion Control

arXiv: https://arxiv.org/abs/2610.06002 · HTML: https://mlsanity.com/paper/2610.06002/

## Key facts

- No citing papers in the map yet (data through 14 Oct 2026).
- Placed in Diffusion and flow policies for robotics, one of 14 directions in Diffusion models.
- Builds on 35 of its 55 references that are in the map.
- First posted on arXiv 5 Oct 2026.

## Placed in

- Diffusion models / [Diffusion and flow policies for robotics](https://mlsanity.com/diffusion/diffusion-and-flow-policies-for-robotics/)

## Builds on (most cited first, 30 of 35)

- [Diffusion Models Beat GANs on Image Synthesis](https://mlsanity.com/paper/2105.05233/) (2021)
- [Diffusion Policy: Visuomotor Policy Learning via Action Diffusion](https://mlsanity.com/paper/2303.04137/) (2023)
- [SDEdit: Guided Image Synthesis and Editing with Stochastic Differential Equations](https://mlsanity.com/paper/2108.01073/) (2021)
- [Learning Fine-Grained Bimanual Manipulation with Low-Cost Hardware](https://mlsanity.com/paper/2304.13705/) (2023)
- [D4RL: Datasets for Deep Data-Driven Reinforcement Learning](https://mlsanity.com/paper/2004.07219/) (2020)
- [Planning with Diffusion for Flexible Behavior Synthesis](https://mlsanity.com/paper/2205.09991/) (2022)
- [Deep Reinforcement Learning in a Handful of Trials using Probabilistic Dynamics Models](https://mlsanity.com/paper/1805.12114/) (2018)
- [Is Conditional Generative Modeling all you need for Decision-Making?](https://mlsanity.com/paper/2211.15657/) (2022)
- [Behavior Transformers: Cloning k modes with one stone](https://mlsanity.com/paper/2206.11251/) (2022)
- [Diffusion probabilistic modeling of protein backbones in 3D for the motif-scaffolding problem](https://mlsanity.com/paper/2206.04119/) (2022)
- [Inference-Time Scaling for Diffusion Models beyond Scaling Denoising Steps](https://mlsanity.com/paper/2501.09732/) (2025)
- [Practical and Asymptotically Exact Conditional Sampling in Diffusion Models](https://mlsanity.com/paper/2306.17775/) (2023)
- [A General Framework for Inference-time Scaling and Steering of Diffusion Models](https://mlsanity.com/paper/2501.06848/) (2025)
- [Real-Time Execution of Action Chunking Flow Policies](https://mlsanity.com/paper/2506.07339/) (2025)
- [Motion Planning Diffusion: Learning and Planning of Robot Motions with Diffusion Models](https://mlsanity.com/paper/2308.01557/) (2023)
- [Derivative-Free Guidance in Continuous and Discrete Diffusion Models with Soft Value-Based Decoding](https://mlsanity.com/paper/2408.08252/) (2024)
- [Feynman-Kac Correctors in Diffusion: Annealing, Guidance, and Product of Experts](https://mlsanity.com/paper/2503.02819/) (2025)
- [Test-time Alignment of Diffusion Models without Reward Over-optimization](https://mlsanity.com/paper/2501.05803/) (2025)
- [Probabilistic Inference in Language Models via Twisted Sequential Monte Carlo](https://mlsanity.com/paper/2404.17546/) (2024)
- [Constrained Synthesis with Projected Diffusion Models](https://mlsanity.com/paper/2402.03559/) (2024)
- [Reflected Diffusion Models](https://mlsanity.com/paper/2304.04740/) (2023)
- [SafeDiffuser: Safe Planning with Diffusion Probabilistic Models](https://mlsanity.com/paper/2306.00148/) (2023)
- [Particle Guidance: non-I.I.D. Diverse Sampling with Diffusion Models](https://mlsanity.com/paper/2310.13102/) (2023)
- [Diffusion Models for Constrained Domains](https://mlsanity.com/paper/2304.05364/) (2023)
- [Streaming Diffusion Policy: Fast Policy Synthesis with Variable Noise Diffusion Models](https://mlsanity.com/paper/2406.04806/) (2024)
- [Towards Diverse Behaviors: A Benchmark for Imitation Learning with Human Demonstrations](https://mlsanity.com/paper/2402.14606/) (2024)
- [Bidirectional Decoding: Improving Action Chunking via Guided Test-Time Sampling](https://mlsanity.com/paper/2408.17355/) (2024)
- [Adaptive Online Replanning with Diffusion Models](https://mlsanity.com/paper/2310.09629/) (2023)
- [Diffusion Predictive Control with Constraints](https://mlsanity.com/paper/2412.09342/) (2024)
- [Model-Based Diffusion for Trajectory Optimization](https://mlsanity.com/paper/2407.01573/) (2024)

## Abstract (arXiv)

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.