# Compositional Diffusion-Based Continuous Constraint Solvers

arXiv: https://arxiv.org/abs/2309.00966 · HTML: https://mlsanity.com/paper/2309.00966/

## Key facts

- Cited by 40 papers in the map (data through 14 Oct 2026).
- Builds on 27 of its 36 references that are in the map.
- First posted on arXiv 2 Sep 2023.

## Builds on (most cited first, 27 of 27)

- [Improved Denoising Diffusion Probabilistic Models](https://mlsanity.com/paper/2102.09672/) (2021)
- [ShapeNet: An Information-Rich 3D Model Repository](https://mlsanity.com/paper/1512.03012/) (2015)
- [Compositional Visual Generation with Composable Diffusion Models](https://mlsanity.com/paper/2206.01714/) (2022)
- [CLIPort: What and Where Pathways for Robotic Manipulation](https://mlsanity.com/paper/2109.12098/) (2021)
- [SAPIEN: A SimulAted Part-based Interactive ENvironment](https://mlsanity.com/paper/2003.08515/) (2020)
- [Learning Latent Plans from Play](https://mlsanity.com/paper/1903.01973/) (2019)
- [Integrated Task and Motion Planning](https://mlsanity.com/paper/2010.01083/) (2020)
- [6-DOF GraspNet: Variational Grasp Generation for Object Manipulation](https://mlsanity.com/paper/1905.10520/) (2019)
- [Reduce, Reuse, Recycle: Compositional Generation with Energy-Based Diffusion Models and MCMC](https://mlsanity.com/paper/2302.11552/) (2023)
- [PDDLStream: Integrating Symbolic Planners and Blackbox Samplers via Optimistic Adaptive Planning](https://mlsanity.com/paper/1802.08705/) (2018)
- [What Matters in Language Conditioned Robotic Imitation Learning over Unstructured Data](https://mlsanity.com/paper/2204.06252/) (2022)
- [Learning to Compose Visual Relations](https://mlsanity.com/paper/2111.09297/) (2021)
- [Controllable and Compositional Generation with Latent-Space Energy-Based Models](https://mlsanity.com/paper/2110.10873/) (2021)
- [StructFormer: Learning Spatial Structure for Language-Guided Semantic Rearrangement of Novel Objects](https://mlsanity.com/paper/2110.10189/) (2021)
- [SE(3)-Equivariant Relational Rearrangement with Neural Descriptor Fields](https://mlsanity.com/paper/2211.09786/) (2022)
- [StructDiffusion: Language-Guided Creation of Physically-Valid Structures using Unseen Objects](https://mlsanity.com/paper/2211.04604/) (2022)
- [Global Planning for Contact-Rich Manipulation via Local Smoothing of Quasi-dynamic Contact Models](https://mlsanity.com/paper/2206.10787/) (2022)
- [SORNet: Spatial Object-Centric Representations for Sequential Manipulation](https://mlsanity.com/paper/2109.03891/) (2021)
- [Long-Horizon Manipulation of Unknown Objects via Task and Motion Planning with Estimated Affordances](https://mlsanity.com/paper/2108.04145/) (2021)
- [Energy-based Models are Zero-Shot Planners for Compositional Scene Rearrangement](https://mlsanity.com/paper/2304.14391/) (2023)
- [Predicting Stable Configurations for Semantic Placement of Novel Objects](https://mlsanity.com/paper/2108.12062/) (2021)
- [A Long Horizon Planning Framework for Manipulating Rigid Pointcloud Objects](https://mlsanity.com/paper/2011.08177/) (2020)
- [Stable bin packing of non-convex 3D objects with a robot manipulator](https://mlsanity.com/paper/1812.04093/) (2018)
- [Sequence-Based Plan Feasibility Prediction for Efficient Task and Motion Planning](https://mlsanity.com/paper/2211.01576/) (2022)
- [Composable Energy Policies for Reactive Motion Generation and Reinforcement Learning](https://mlsanity.com/paper/2105.04962/) (2021)
- [ZeroC: A Neuro-Symbolic Model for Zero-shot Concept Recognition and Acquisition at Inference Time](https://mlsanity.com/paper/2206.15049/) (2022)
- [Learning Perceptual Concepts by Bootstrapping from Human Queries](https://mlsanity.com/paper/2111.05251/) (2021)

## Built on by (most cited first, 30 of 40)

- [ReKep: Spatio-Temporal Reasoning of Relational Keypoint Constraints for Robotic Manipulation](https://mlsanity.com/paper/2409.01652/) (2024)
- [Video Language Planning](https://mlsanity.com/paper/2310.10625/) (2023)
- [RoboEXP: Action-Conditioned Scene Graph via Interactive Exploration for Robotic Manipulation](https://mlsanity.com/paper/2402.15487/) (2024)
- [PoCo: Policy Composition from and for Heterogeneous Robot Learning](https://mlsanity.com/paper/2402.02511/) (2024)
- [Compositional Generative Modeling: A Single Model is Not All You Need](https://mlsanity.com/paper/2402.01103/) (2024)
- [Potential Based Diffusion Motion Planning](https://mlsanity.com/paper/2407.06169/) (2024)
- [Generative Trajectory Stitching through Diffusion Composition](https://mlsanity.com/paper/2503.05153/) (2025)
- [Diffusion Models for Robotic Manipulation: A Survey](https://mlsanity.com/paper/2504.08438/) (2025)
- [Inference-Time Policy Steering through Human Interactions](https://mlsanity.com/paper/2411.16627/) (2024)
- [Learning Iterative Reasoning through Energy Diffusion](https://mlsanity.com/paper/2406.11179/) (2024)
- [Deep Generative Models in Robotics: A Survey on Learning from Multimodal Demonstrations](https://mlsanity.com/paper/2408.04380/) (2024)
- [Model-Based Diffusion for Trajectory Optimization](https://mlsanity.com/paper/2407.01573/) (2024)
- [PoE-World: Compositional World Modeling with Products of Programmatic Experts](https://mlsanity.com/paper/2505.10819/) (2025)
- [Practice Makes Perfect: Planning to Learn Skill Parameter Policies](https://mlsanity.com/paper/2402.15025/) (2024)
- [Compositional Generative Inverse Design](https://mlsanity.com/paper/2401.13171/) (2024)
- [DiffuSolve: Diffusion-based Solver for Non-convex Trajectory Optimization](https://mlsanity.com/paper/2403.05571/) (2024)
- [Trust the PRoC3S: Solving Long-Horizon Robotics Problems with LLMs and Constraint Satisfaction](https://mlsanity.com/paper/2406.05572/) (2024)
- [Mechanisms of Projective Composition of Diffusion Models](https://mlsanity.com/paper/2502.04549/) (2025)
- [Multi-Modal Manipulation via Multi-Modal Policy Consensus](https://mlsanity.com/paper/2509.23468/) (2025)
- [Constraint-Aware Diffusion Models for Trajectory Optimization](https://mlsanity.com/paper/2406.00990/) (2024)
- ["Set It Up!": Functional Object Arrangement with Compositional Generative Models](https://mlsanity.com/paper/2405.11928/) (2024)
- [TeLoGraF: Temporal Logic Planning via Graph-encoded Flow Matching](https://mlsanity.com/paper/2505.00562/) (2025)
- [DISCO: Language-Guided Manipulation with Diffusion Policies and Constrained Inpainting](https://mlsanity.com/paper/2406.09767/) (2024)
- [Modality-Composable Diffusion Policy via Inference-Time Distribution-level Composition](https://mlsanity.com/paper/2503.12466/) (2025)
- [Aligning Diffusion Model with Problem Constraints for Trajectory Optimization](https://mlsanity.com/paper/2504.00342/) (2025)
- [Projected Coupled Diffusion for Test-Time Constrained Joint Generation](https://mlsanity.com/paper/2508.10531/) (2025)
- [Flexible Multitask Learning with Factorized Diffusion Policy](https://mlsanity.com/paper/2512.21898/) (2025)
- [Prime the search: Using large language models for guiding geometric task and motion planning by warm-starting tree search](https://mlsanity.com/paper/2506.07062/) (2025)
- [Composing Diffusion Policies for Few-shot Learning of Movement Trajectories](https://mlsanity.com/paper/2410.17479/) (2024)
- [Local Mechanisms of Compositional Generalization in Conditional Diffusion](https://mlsanity.com/paper/2509.16447/) (2025)

## Abstract (arXiv)

This paper introduces an approach for learning to solve continuous constraint satisfaction problems (CCSP) in robotic reasoning and planning. Previous methods primarily rely on hand-engineering or learning generators for specific constraint types and then rejecting the value assignments when other constraints are violated. By contrast, our model, the compositional diffusion continuous constraint solver (Diffusion-CCSP) derives global solutions to CCSPs by representing them as factor graphs and combining the energies of diffusion models trained to sample for individual constraint types. Diffusion-CCSP exhibits strong generalization to novel combinations of known constraints, and it can be integrated into a task and motion planner to devise long-horizon plans that include actions with both discrete and continuous parameters. Project site: https://diffusion-ccsp.github.io/