# D-Cubed: Latent Diffusion Trajectory Optimisation for Dexterous Deformable Manipulation

arXiv: https://arxiv.org/abs/2403.12861 · HTML: https://mlsanity.com/paper/2403.12861/

## 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 38 of its 52 references that are in the map.
- First posted on arXiv 19 Mar 2024.

## 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 38)

- [Denoising Diffusion Probabilistic Models](https://mlsanity.com/paper/2006.11239/) (2020)
- [Proximal Policy Optimization Algorithms](https://mlsanity.com/paper/1707.06347/) (2017)
- [Score-Based Generative Modeling through Stochastic Differential Equations](https://mlsanity.com/paper/2011.13456/) (2020)
- [Diffusion Models Beat GANs on Image Synthesis](https://mlsanity.com/paper/2105.05233/) (2021)
- [Deep Unsupervised Learning using Nonequilibrium Thermodynamics](https://mlsanity.com/paper/1503.03585/) (2015)
- [Hierarchical Text-Conditional Image Generation with CLIP Latents](https://mlsanity.com/paper/2204.06125/) (2022)
- [Diffusion Policy: Visuomotor Policy Learning via Action Diffusion](https://mlsanity.com/paper/2303.04137/) (2023)
- [Planning with Diffusion for Flexible Behavior Synthesis](https://mlsanity.com/paper/2205.09991/) (2022)
- [Isaac Gym: High Performance GPU-Based Physics Simulation For Robot Learning](https://mlsanity.com/paper/2108.10470/) (2021)
- [Deep Reinforcement Learning at the Edge of the Statistical Precipice](https://mlsanity.com/paper/2108.13264/) (2021)
- [Solving Rubik's Cube with a Robot Hand](https://mlsanity.com/paper/1910.07113/) (2019)
- [Learning Complex Dexterous Manipulation with Deep Reinforcement Learning and Demonstrations](https://mlsanity.com/paper/1709.10087/) (2017)
- [SAPIEN: A SimulAted Part-based Interactive ENvironment](https://mlsanity.com/paper/2003.08515/) (2020)
- [Accelerating Reinforcement Learning with Learned Skill Priors](https://mlsanity.com/paper/2010.11944/) (2020)
- [Deep Dynamics Models for Learning Dexterous Manipulation](https://mlsanity.com/paper/1909.11652/) (2019)
- [A System for General In-Hand Object Re-Orientation](https://mlsanity.com/paper/2111.03043/) (2021)
- [AdaptDiffuser: Diffusion Models as Adaptive Self-evolving Planners](https://mlsanity.com/paper/2302.01877/) (2023)
- [SoftGym: Benchmarking Deep Reinforcement Learning for Deformable Object Manipulation](https://mlsanity.com/paper/2011.07215/) (2020)
- [DexPilot: Vision Based Teleoperation of Dexterous Robotic Hand-Arm System](https://mlsanity.com/paper/1910.03135/) (2019)
- [PlasticineLab: A Soft-Body Manipulation Benchmark with Differentiable Physics](https://mlsanity.com/paper/2104.03311/) (2021)
- [Sample-efficient Cross-Entropy Method for Real-time Planning](https://mlsanity.com/paper/2008.06389/) (2020)
- [LEAP Hand: Low-Cost, Efficient, and Anthropomorphic Hand for Robot Learning](https://mlsanity.com/paper/2309.06440/) (2023)
- [RoboCook: Long-Horizon Elasto-Plastic Object Manipulation with Diverse Tools](https://mlsanity.com/paper/2306.14447/) (2023)
- [RoboCraft: Learning to See, Simulate, and Shape Elasto-Plastic Objects with Graph Networks](https://mlsanity.com/paper/2205.02909/) (2022)
- [Sinkhorn Divergences for Unbalanced Optimal Transport](https://mlsanity.com/paper/1910.12958/) (2019)
- [PlayFusion: Skill Acquisition via Diffusion from Language-Annotated Play](https://mlsanity.com/paper/2312.04549/) (2023)
- [Denoising Likelihood Score Matching for Conditional Score-based Data Generation](https://mlsanity.com/paper/2203.14206/) (2022)
- [DiffSkill: Skill Abstraction from Differentiable Physics for Deformable Object Manipulations with Tools](https://mlsanity.com/paper/2203.17275/) (2022)
- [Diffusion-ES: Gradient-free Planning with Diffusion for Autonomous Driving and Zero-Shot Instruction Following](https://mlsanity.com/paper/2402.06559/) (2024)
- [Differentiable Simulation of Soft Multi-body Systems](https://mlsanity.com/paper/2205.01758/) (2022)

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

- [M2Diffuser: Diffusion-based Trajectory Optimization for Mobile Manipulation in 3D Scenes](https://mlsanity.com/paper/2410.11402/) (2024)
- [Robustness without Wrinkles: Parallel Simulation and Robust MPC for Certified Deformable Manipulation](https://mlsanity.com/paper/2606.14188/) (2026)
- [Grasp-MPC: Closed-Loop Visual Grasping via Value-Guided Model Predictive Control](https://mlsanity.com/paper/2509.06201/) (2025)
- [LeWAM: End-to-End World and Action Modeling with JEPAs](https://mlsanity.com/paper/2610.12818/) (2026)

## Abstract (arXiv)

Mastering dexterous robotic manipulation of deformable objects is vital for overcoming the limitations of parallel grippers in real-world applications. Current trajectory optimisation approaches often struggle to solve such tasks due to the large search space and the limited task information available from a cost function. In this work, we propose D-Cubed, a novel trajectory optimisation method using a latent diffusion model (LDM) trained from a task-agnostic play dataset to solve dexterous deformable object manipulation tasks. D-Cubed learns a skill-latent space that encodes short-horizon actions in the play dataset using a VAE and trains a LDM to compose the skill latents into a skill trajectory, representing a long-horizon action trajectory in the dataset. To optimise a trajectory for a target task, we introduce a novel gradient-free guided sampling method that employs the Cross-Entropy method within the reverse diffusion process. In particular, D-Cubed samples a small number of noisy skill trajectories using the LDM for exploration and evaluates the trajectories in simulation. Then, D-Cubed selects the trajectory with the lowest cost for the subsequent reverse process. This effectively explores promising solution areas and optimises the sampled trajectories towards a target task throughout the reverse diffusion process. Through empirical evaluation on a public benchmark of dexterous deformable object manipulation tasks, we demonstrate that D-Cubed outperforms traditional trajectory optimisation and competitive baseline approaches by a significant margin. We further demonstrate that trajectories found by D-Cubed readily transfer to a real-world LEAP hand on a folding task.