# Parallelised Diffeomorphic Sampling-based Motion Planning

arXiv: https://arxiv.org/abs/2108.11775 · HTML: https://mlsanity.com/paper/2108.11775/

## Key facts

- Cited by 16 papers in the map (data through 14 Oct 2026).
- Builds on 12 of its 32 references that are in the map.
- First posted on arXiv 26 Aug 2021.

## Builds on (most cited first, 12 of 12)

- [DeepSDF: Learning Continuous Signed Distance Functions for Shape Representation](https://mlsanity.com/paper/1901.05103/) (2019)
- [Variational Inference with Normalizing Flows](https://mlsanity.com/paper/1505.05770/) (2015)
- [Normalizing Flows for Probabilistic Modeling and Inference](https://mlsanity.com/paper/1912.02762/) (2019)
- [Neural Spline Flows](https://mlsanity.com/paper/1906.04032/) (2019)
- [Analyzing Inverse Problems with Invertible Neural Networks](https://mlsanity.com/paper/1808.04730/) (2018)
- [PRIMAL: Pathfinding via Reinforcement and Imitation Multi-Agent Learning](https://mlsanity.com/paper/1809.03531/) (2018)
- [Learning Sampling Distributions for Robot Motion Planning](https://mlsanity.com/paper/1709.05448/) (2017)
- [Balancing Global Exploration and Local-connectivity Exploitation with Rapidly-exploring Random disjointed-Trees](https://mlsanity.com/paper/1810.03749/) (2018)
- [Bayesian Local Sampling-based Planning](https://mlsanity.com/paper/1909.03452/) (2019)
- [Informed Sampling for Asymptotically Optimal Path Planning (Consolidated Version)](https://mlsanity.com/paper/1706.06454/) (2017)
- [Learning to Plan Optimally with Flow-based Motion Planner](https://mlsanity.com/paper/2010.11323/) (2020)
- [Rapidly-exploring Random Forest: Adaptively Exploits Local Structure with Generalised Multi-Trees Motion Planning](https://mlsanity.com/paper/2103.04487/) (2021)

## Built on by (most cited first, 16 of 16)

- [Deep Generative Models in Robotics: A Survey on Learning from Multimodal Demonstrations](https://mlsanity.com/paper/2408.04380/) (2024)
- [RecGS: Removing Water Caustic with Recurrent Gaussian Splatting](https://mlsanity.com/paper/2407.10318/) (2024)
- [Instructing Robots by Sketching: Learning from Demonstration via Probabilistic Diagrammatic Teaching](https://mlsanity.com/paper/2309.03835/) (2023)
- [Variational Inference MPC using Normalizing Flows and Out-of-Distribution Projection](https://mlsanity.com/paper/2205.04667/) (2022)
- [Learning Sampling Distributions for Model Predictive Control](https://mlsanity.com/paper/2212.02587/) (2022)
- [SplaTraj: Camera Trajectory Generation with Semantic Gaussian Splatting](https://mlsanity.com/paper/2410.06014/) (2024)
- [Parallel Stochastic Gradient-Based Planning for World Models](https://mlsanity.com/paper/2602.00475/) (2026)
- [PhotoReg: Photometrically Registering 3D Gaussian Splatting Models](https://mlsanity.com/paper/2410.05044/) (2024)
- [DOSE3 : Diffusion-based Out-of-distribution detection on SE(3) trajectories](https://mlsanity.com/paper/2502.16725/) (2025)
- [L4KDE: Learning for KinoDynamic Tree Expansion](https://mlsanity.com/paper/2203.00975/) (2022)
- [3D Foundation Models Enable Simultaneous Geometry and Pose Estimation of Grasped Objects](https://mlsanity.com/paper/2407.10331/) (2024)
- [Discover Life Skills for Planning with Bandits via Observing and Learning How the World Works](https://mlsanity.com/paper/2207.08130/) (2022)
- [Cross-Modal Instructions for Robot Motion Generation](https://mlsanity.com/paper/2509.21107/) (2025)
- [Toward Generalist Neural Motion Planners for Robotic Manipulators: Challenges and Opportunities](https://mlsanity.com/paper/2603.24318/) (2026)
- [Learning to Represent Surroundings, Anticipate Motion and Take Informed Actions in Unstructured Environments](https://mlsanity.com/paper/2407.10383/) (2024)
- [Enhancing Path Planning Performance through Image Representation Learning of High-Dimensional Configuration Spaces](https://mlsanity.com/paper/2501.06639/) (2025)

## Abstract (arXiv)

We propose Parallelised Diffeomorphic Sampling-based Motion Planning (PDMP). PDMP is a novel parallelised framework that uses bijective and differentiable mappings, or diffeomorphisms, to transform sampling distributions of sampling-based motion planners, in a manner akin to normalising flows. Unlike normalising flow models which use invertible neural network structures to represent these diffeomorphisms, we develop them from gradient information of desired costs, and encode desirable behaviour, such as obstacle avoidance. These transformed sampling distributions can then be used for sampling-based motion planning. A particular example is when we wish to imbue the sampling distribution with knowledge of the environment geometry, such that drawn samples are less prone to be in collisions. To this end, we propose to learn a continuous occupancy representation from environment occupancy data, such that gradients of the representation defines a valid diffeomorphism and is amenable to fast parallel evaluation. We use this to "morph" the sampling distribution to draw far fewer collision-prone samples. PDMP is able to leverage gradient information of costs, to inject specifications, in a manner similar to optimisation-based motion planning methods, but relies on drawing from a sampling distribution, retaining the tendency to find more global solutions, thereby bridging the gap between trajectory optimisation and sampling-based planning methods.