# Factored Diffusion Policies:Compositionally Generalized Robot Control with a Single Score Network

arXiv: https://arxiv.org/abs/2605.22596 · HTML: https://mlsanity.com/paper/2605.22596/

## Key facts

- Cited by 2 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 32 references that are in the map.
- First posted on arXiv 21 May 2026.

## 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 Implicit Models](https://mlsanity.com/paper/2010.02502/) (2020)
- [Score-Based Generative Modeling through Stochastic Differential Equations](https://mlsanity.com/paper/2011.13456/) (2020)
- [Classifier-Free Diffusion Guidance](https://mlsanity.com/paper/2207.12598/) (2022)
- [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)
- [Domain Randomization for Transferring Deep Neural Networks from Simulation to the Real World](https://mlsanity.com/paper/1703.06907/) (2017)
- [Compositional Visual Generation with Composable Diffusion Models](https://mlsanity.com/paper/2206.01714/) (2022)
- [Sampling is as easy as learning the score: theory for diffusion models with minimal data assumptions](https://mlsanity.com/paper/2209.11215/) (2022)
- [Efficient and Accurate Estimation of Lipschitz Constants for Deep Neural Networks](https://mlsanity.com/paper/1906.04893/) (2019)
- [Nearly d-Linear Convergence Bounds for Diffusion Models via Stochastic Localization](https://mlsanity.com/paper/2308.03686/) (2023)
- [CAD2RL: Real Single-Image Flight without a Single Real Image](https://mlsanity.com/paper/1611.04201/) (2016)
- [Reduce, Reuse, Recycle: Compositional Generation with Energy-Based Diffusion Models and MCMC](https://mlsanity.com/paper/2302.11552/) (2023)
- [Multimodal Diffusion Transformer: Learning Versatile Behavior from Multimodal Goals](https://mlsanity.com/paper/2407.05996/) (2024)
- [Reaching the Limit in Autonomous Racing: Optimal Control versus Reinforcement Learning](https://mlsanity.com/paper/2310.10943/) (2023)
- [Generative Skill Chaining: Long-Horizon Skill Planning with Diffusion Models](https://mlsanity.com/paper/2401.03360/) (2023)
- [SkillDiffuser: Interpretable Hierarchical Planning via Skill Abstractions in Diffusion-Based Task Execution](https://mlsanity.com/paper/2312.11598/) (2023)
- [Concept Algebra for (Score-Based) Text-Controlled Generative Models](https://mlsanity.com/paper/2302.03693/) (2023)
- [PoCo: Policy Composition from and for Heterogeneous Robot Learning](https://mlsanity.com/paper/2402.02511/) (2024)
- [Reachability Analysis of Neural Feedback Loops](https://mlsanity.com/paper/2108.04140/) (2021)
- [Time-Optimal Planning for Quadrotor Waypoint Flight](https://mlsanity.com/paper/2108.04537/) (2021)
- [Compose Your Policies! Improving Diffusion-based or Flow-based Robot Policies via Test-time Distribution-level Composition](https://mlsanity.com/paper/2510.01068/) (2025)
- [CoInD: Enabling Logical Compositions in Diffusion Models](https://mlsanity.com/paper/2503.01145/) (2025)
- [Modality-Composable Diffusion Policy via Inference-Time Distribution-level Composition](https://mlsanity.com/paper/2503.12466/) (2025)
- [Flexible Multitask Learning with Factorized Diffusion Policy](https://mlsanity.com/paper/2512.21898/) (2025)
- [Composing Diffusion Policies for Few-shot Learning of Movement Trajectories](https://mlsanity.com/paper/2410.17479/) (2024)

## Built on by (most cited first, 2 of 2)

- [AURA: Action-Gated Memory for Robot Policies at Constant VRAM](https://mlsanity.com/paper/2606.02775/) (2026)
- [Akule: Fast and Scalable Multi-Robot Motion Planning via Sparse Interaction Diffusion](https://mlsanity.com/paper/2610.14248/) (2026)

## Abstract (arXiv)

Robotic tasks are typically specified by a tuple of factors, such as the object to be grasped, the obstacles to be avoided, the color of the target, and so on. Collecting expert demonstrations for every combination of factor values grows combinatorially. We present factored diffusion policies: a single shared diffusion network trained with per-factor null-token dropout, whose score decomposes additively across factors at inference. Under approximate conditional independence between factors given the action-observation pair, this composition approximates the true joint score with a bounded uniform error, reducing the training-task budget from a product of factor cardinalities to a sum. A trajectory-tube certificate chains this score-level bound through the reverse-time sampling ODE and a contracting tracking controller into a closed-loop state-trajectory tube whose radius factors into an ODE-sensitivity constant and a per-factor score-error budget. Unlike compositional-diffusion methods for control that combine separately trained networks, we use one shared network. Drone racing experiments confirm both the generalization bound and the certificate. On state-based multi-gate racing, the factored policy passes 90% of held-out gates -- matching an oracle -- while a K-network composition baseline collapses to 3%; on vision-based single-gate traversal, it transfers zero-shot to an unseen venue with +11.7pp success-rate gain and 2.4X crash-rate reduction.