# KDPE: A Kernel Density Estimation Strategy for Diffusion Policy Trajectory Selection

arXiv: https://arxiv.org/abs/2508.10511 · HTML: https://mlsanity.com/paper/2508.10511/

## Key facts

- Cited by 4 papers in the map (data through 14 Oct 2026).
- Placed in Diffusion and flow policies for robotics, one of 14 directions in Diffusion models.
- Builds on 25 of its 37 references that are in the map.
- First posted on arXiv 14 Aug 2025.

## 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, 25 of 25)

- [Denoising Diffusion Probabilistic Models](https://mlsanity.com/paper/2006.11239/) (2020)
- [Denoising Diffusion Implicit Models](https://mlsanity.com/paper/2010.02502/) (2020)
- [OpenVLA: An Open-Source Vision-Language-Action Model](https://mlsanity.com/paper/2406.09246/) (2024)
- [Diffusion Policy: Visuomotor Policy Learning via Action Diffusion](https://mlsanity.com/paper/2303.04137/) (2023)
- [π0: A Vision-Language-Action Flow Model for General Robot Control](https://mlsanity.com/paper/2410.24164/) (2024)
- [RT-1: Robotics Transformer for Real-World Control at Scale](https://mlsanity.com/paper/2212.06817/) (2022)
- [Scaling LLM Test-Time Compute Optimally can be More Effective than Scaling Model Parameters](https://mlsanity.com/paper/2408.03314/) (2024)
- [π0.5: a Vision-Language-Action Model with Open-World Generalization](https://mlsanity.com/paper/2504.16054/) (2025)
- [Octo: An Open-Source Generalist Robot Policy](https://mlsanity.com/paper/2405.12213/) (2024)
- [On the Continuity of Rotation Representations in Neural Networks](https://mlsanity.com/paper/1812.07035/) (2018)
- [Large Language Monkeys: Scaling Inference Compute with Repeated Sampling](https://mlsanity.com/paper/2407.21787/) (2024)
- [What Matters in Learning from Offline Human Demonstrations for Robot Manipulation](https://mlsanity.com/paper/2108.03298/) (2021)
- [MimicGen: A Data Generation System for Scalable Robot Learning using Human Demonstrations](https://mlsanity.com/paper/2310.17596/) (2023)
- [Goal-Conditioned Imitation Learning using Score-based Diffusion Policies](https://mlsanity.com/paper/2304.02532/) (2023)
- [Inference-Time Scaling for Diffusion Models beyond Scaling Denoising Steps](https://mlsanity.com/paper/2501.09732/) (2025)
- [SANA 1.5: Efficient Scaling of Training-Time and Inference-Time Compute in Linear Diffusion Transformer](https://mlsanity.com/paper/2501.18427/) (2025)
- [Scaling Up and Distilling Down: Language-Guided Robot Skill Acquisition](https://mlsanity.com/paper/2307.14535/) (2023)
- [RoboCat: A Self-Improving Generalist Agent for Robotic Manipulation](https://mlsanity.com/paper/2306.11706/) (2023)
- [Steering Your Generalists: Improving Robotic Foundation Models via Value Guidance](https://mlsanity.com/paper/2410.13816/) (2024)
- [Bootstrap Your Own Skills: Learning to Solve New Tasks with Large Language Model Guidance](https://mlsanity.com/paper/2310.10021/) (2023)
- [The Ingredients for Robotic Diffusion Transformers](https://mlsanity.com/paper/2410.10088/) (2024)
- [Unpacking Failure Modes of Generative Policies: Runtime Monitoring of Consistency and Progress](https://mlsanity.com/paper/2410.04640/) (2024)
- [Reflect-DiT: Inference-Time Scaling for Text-to-Image Diffusion Transformers via In-Context Reflection](https://mlsanity.com/paper/2503.12271/) (2025)
- [Diffusion Meets DAgger: Supercharging Eye-in-hand Imitation Learning](https://mlsanity.com/paper/2402.17768/) (2024)
- [RoboMD: Uncovering Robot Vulnerabilities through Semantic Potential Fields](https://mlsanity.com/paper/2412.02818/) (2024)

## Built on by (most cited first, 4 of 4)

- [Rewind-IL: Online Failure Detection and State Respawning for Imitation Learning](https://mlsanity.com/paper/2604.16683/) (2026)
- [HiTac-WAM: A Hierarchical Tactile World Action Model for Contact-Rich Robot Manipulation](https://mlsanity.com/paper/2608.19574/) (2026)
- [Geometry Guided Self-Consistency for Physical AI](https://mlsanity.com/paper/2605.08638/) (2026)
- [DiVeR: Decision-Critical Verifier Learning for VLA Test-Time Scaling](https://mlsanity.com/paper/2610.04933/) (2026)

## Abstract (arXiv)

Learning robot policies that capture multimodality in the training data has been a long-standing open challenge for behavior cloning. Recent approaches tackle the problem by modeling the conditional action distribution with generative models. One of these approaches is Diffusion Policy, which relies on a diffusion model to denoise random points into robot action trajectories. While achieving state-of-the-art performance, it has two main drawbacks that may lead the robot out of the data distribution during policy execution. First, the stochasticity of the denoising process can highly impact on the quality of generated trajectory of actions. Second, being a supervised learning approach, it can learn data outliers from the dataset used for training. Recent work focuses on mitigating these limitations by combining Diffusion Policy either with large-scale training or with classical behavior cloning algorithms. Instead, we propose KDPE, a Kernel Density Estimation-based strategy that filters out potentially harmful trajectories output of Diffusion Policy while keeping a low test-time computational overhead. For Kernel Density Estimation, we propose a manifold-aware kernel to model a probability density function for actions composed of end-effector Cartesian position, orientation, and gripper state. KDPE overall achieves better performance than Diffusion Policy on simulated single-arm tasks and real robot experiments. Additional material and code are available on our project page at https://hsp-iit.github.io/KDPE/.