# Diffusion-Based Impedance Learning for Contact-Rich Manipulation Tasks

arXiv: https://arxiv.org/abs/2509.19696 · HTML: https://mlsanity.com/paper/2509.19696/

## Key facts

- Cited by 3 papers in the map (data through 14 Oct 2026).
- Builds on 33 of its 78 references that are in the map.
- First posted on arXiv 24 Sep 2025.

## Builds on (most cited first, 30 of 33)

- [Attention Is All You Need](https://mlsanity.com/paper/1706.03762/) (2017)
- [An Image is Worth 16x16 Words: Transformers for Image Recognition at Scale](https://mlsanity.com/paper/2010.11929/) (2020)
- [Denoising Diffusion Probabilistic Models](https://mlsanity.com/paper/2006.11239/) (2020)
- [Denoising Diffusion Implicit Models](https://mlsanity.com/paper/2010.02502/) (2020)
- [Deep Unsupervised Learning using Nonequilibrium Thermodynamics](https://mlsanity.com/paper/1503.03585/) (2015)
- [Improved Denoising Diffusion Probabilistic Models](https://mlsanity.com/paper/2102.09672/) (2021)
- [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)
- [Perceiver: General Perception with Iterative Attention](https://mlsanity.com/paper/2103.03206/) (2021)
- [Planning with Diffusion for Flexible Behavior Synthesis](https://mlsanity.com/paper/2205.09991/) (2022)
- [Perceiver-Actor: A Multi-Task Transformer for Robotic Manipulation](https://mlsanity.com/paper/2209.05451/) (2022)
- [A Survey of Transformers](https://mlsanity.com/paper/2106.04554/) (2021)
- [Foundation Models for Time Series Analysis: A Tutorial and Survey](https://mlsanity.com/paper/2403.14735/) (2024)
- [Motion Planning Diffusion: Learning and Planning of Robot Motions with Diffusion Models](https://mlsanity.com/paper/2308.01557/) (2023)
- [What Language Model Architecture and Pretraining Objective Work Best for Zero-Shot Generalization?](https://mlsanity.com/paper/2204.05832/) (2022)
- [A Careful Examination of Large Behavior Models for Multitask Dexterous Manipulation](https://mlsanity.com/paper/2507.05331/) (2025)
- [Riemannian Flow Matching Policy for Robot Motion Learning](https://mlsanity.com/paper/2403.10672/) (2024)
- [Affordance-based Robot Manipulation with Flow Matching](https://mlsanity.com/paper/2409.01083/) (2024)
- [Global Planning for Contact-Rich Manipulation via Local Smoothing of Quasi-dynamic Contact Models](https://mlsanity.com/paper/2206.10787/) (2022)
- [Adaptive Compliance Policy: Learning Approximate Compliance for Diffusion Guided Control](https://mlsanity.com/paper/2410.09309/) (2024)
- [Diffusion Models for Robotic Manipulation: A Survey](https://mlsanity.com/paper/2504.08438/) (2025)
- [An Introduction to Flow Matching and Diffusion Models](https://mlsanity.com/paper/2506.02070/) (2025)
- [Bundled Gradients through Contact via Randomized Smoothing](https://mlsanity.com/paper/2109.05143/) (2021)
- [ReorientDiff: Diffusion Model based Reorientation for Object Manipulation](https://mlsanity.com/paper/2303.12700/) (2023)
- [Quantifying the Reality Gap in Robotic Manipulation Tasks](https://mlsanity.com/paper/1811.01484/) (2018)
- [Dexterous Contact-Rich Manipulation via the Contact Trust Region](https://mlsanity.com/paper/2505.02291/) (2025)
- [Real-Time Multi-Contact Model Predictive Control via ADMM](https://mlsanity.com/paper/2109.07076/) (2021)
- [Impedance Primitive-augmented Hierarchical Reinforcement Learning for Sequential Tasks](https://mlsanity.com/paper/2508.19607/) (2025)
- [RMPs for Safe Impedance Control in Contact-Rich Manipulation](https://mlsanity.com/paper/2109.12103/) (2021)
- [Robot Control based on Motor Primitives -- A Comparison of Two Approaches](https://mlsanity.com/paper/2310.18771/) (2023)

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

- [Learning Physical Interaction: A Survey of Tactile- and Force-aware Robot Learning](https://mlsanity.com/paper/2608.07558/) (2026)
- [CR-VLA-Force: Learning Control-aware Compliance VLA Model for Robust Contact-rich Robotic Manipulation](https://mlsanity.com/paper/2609.05832/) (2026)
- [IMPACT: Learning Internal-Model Predictive Control for Forceful Robotic Manipulation](https://mlsanity.com/paper/2606.10818/) (2026)

## Abstract (arXiv)

Learning-based methods excel at robot motion generation but remain limited in contact-rich physical interaction. Impedance control provides stable and safe contact behavior but requires task-specific tuning of stiffness and damping parameters. We present Diffusion-Based Impedance Learning, a framework that bridges these paradigms by combining generative modeling with energy-consistent impedance control. A Transformer-based Diffusion Model, conditioned via cross-attention on measured external wrenches, reconstructs simulated Zero-Force Trajectories (sZFTs) that represent contact-consistent equilibrium behavior. A SLERP-based quaternion noise scheduler preserves geometric consistency for rotations on the unit sphere. The reconstructed sZFT is used by an energy-based estimator to adapt impedance online through directional stiffness and damping modulation. Trained on parkour and robot-assisted therapy demonstrations collected via Apple Vision Pro teleoperation, the model achieves sub-millimeter positional and sub-degree rotational accuracy using only tens of thousands of samples. Deployed in real-time torque control on a KUKA LBR iiwa, the approach enables smooth obstacle traversal and generalizes to unseen tasks, achieving 100% success in multi-geometry peg-in-hole insertion. The code for all experiments is publicly available on GitHub and videos of the experiments are available on the project website.