# GPD: Guided Polynomial Diffusion for Motion Planning

arXiv: https://arxiv.org/abs/2501.18229 · HTML: https://mlsanity.com/paper/2501.18229/

## Key facts

- Cited by 3 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 30 Jan 2025.

## Built on by (most cited first, 3 of 3)

- [Crowd-FM: Learned Optimal Selection of Conditional Flow Matching-generated Trajectories for Crowd Navigation](https://mlsanity.com/paper/2602.06698/) (2026)
- [Primitive-based Truncated Diffusion for Efficient Trajectory Generation of Differential Drive Mobile Manipulators](https://mlsanity.com/paper/2604.04166/) (2026)
- [Sum of Costs Diffusion with Dynamic Guidance for Motion Planning](https://mlsanity.com/paper/2605.24690/) (2026)

## Abstract (arXiv)

Diffusion-based motion planners are becoming popular due to their well-established performance improvements, stemming from sample diversity and the ease of incorporating new constraints directly during inference. However, a primary limitation of the diffusion process is the requirement for a substantial number of denoising steps, especially when the denoising process is coupled with gradient-based guidance. In this paper, we introduce, diffusion in the parametric space of trajectories, where the parameters are represented as Bernstein coefficients. We show that this representation greatly improves the effectiveness of the cost function guidance and the inference speed. We also introduce a novel stitching algorithm that leverages the diversity in diffusion-generated trajectories to produce collision-free trajectories with just a single cost function-guided model. We demonstrate that our approaches outperform current SOTA diffusion-based motion planners for manipulators and provide an ablation study on key components.