# MotionDiffuser: Controllable Multi-Agent Motion Prediction using Diffusion

arXiv: https://arxiv.org/abs/2306.03083 · HTML: https://mlsanity.com/paper/2306.03083/

## Key facts

- Cited by 213 papers in the map (data through 14 Oct 2026).
- Placed in World models for autonomous driving, one of 11 directions in World models.
- Builds on 48 of its 57 references that are in the map.
- First posted on arXiv 5 Jun 2023.

## Placed in

- World models / [World models for autonomous driving](https://mlsanity.com/wm/world-models-for-autonomous-driving/)

## Builds on (most cited first, 30 of 48)

- [Denoising Diffusion Probabilistic Models](https://mlsanity.com/paper/2006.11239/) (2020)
- [High-Resolution Image Synthesis with Latent Diffusion Models](https://mlsanity.com/paper/2112.10752/) (2021)
- [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)
- [Hierarchical Text-Conditional Image Generation with CLIP Latents](https://mlsanity.com/paper/2204.06125/) (2022)
- [Photorealistic Text-to-Image Diffusion Models with Deep Language Understanding](https://mlsanity.com/paper/2205.11487/) (2022)
- [Classifier-Free Diffusion Guidance](https://mlsanity.com/paper/2207.12598/) (2022)
- [Neural Ordinary Differential Equations](https://mlsanity.com/paper/1806.07366/) (2018)
- [Improved Denoising Diffusion Probabilistic Models](https://mlsanity.com/paper/2102.09672/) (2021)
- [Elucidating the Design Space of Diffusion-Based Generative Models](https://mlsanity.com/paper/2206.00364/) (2022)
- [DreamFusion: Text-to-3D using 2D Diffusion](https://mlsanity.com/paper/2209.14988/) (2022)
- [Video Diffusion Models](https://mlsanity.com/paper/2204.03458/) (2022)
- [Decoupled Weight Decay Regularization](https://mlsanity.com/paper/1711.05101/) (2017)
- [Imagen Video: High Definition Video Generation with Diffusion Models](https://mlsanity.com/paper/2210.02303/) (2022)
- [Planning with Diffusion for Flexible Behavior Synthesis](https://mlsanity.com/paper/2205.09991/) (2022)
- [Denoising Diffusion Restoration Models](https://mlsanity.com/paper/2201.11793/) (2022)
- [MotionDiffuse: Text-Driven Human Motion Generation with Diffusion Model](https://mlsanity.com/paper/2208.15001/) (2022)
- [ILVR: Conditioning Method for Denoising Diffusion Probabilistic Models](https://mlsanity.com/paper/2108.02938/) (2021)
- [FFJORD: Free-form Continuous Dynamics for Scalable Reversible Generative Models](https://mlsanity.com/paper/1810.01367/) (2018)
- [Large Scale Interactive Motion Forecasting for Autonomous Driving : The Waymo Open Motion Dataset](https://mlsanity.com/paper/2104.10133/) (2021)
- [Improving Diffusion Models for Inverse Problems using Manifold Constraints](https://mlsanity.com/paper/2206.00941/) (2022)
- [MultiPath: Multiple Probabilistic Anchor Trajectory Hypotheses for Behavior Prediction](https://mlsanity.com/paper/1910.05449/) (2019)
- [Come-Closer-Diffuse-Faster: Accelerating Conditional Diffusion Models for Inverse Problems through Stochastic Contraction](https://mlsanity.com/paper/2112.05146/) (2021)
- [Wayformer: Motion Forecasting via Simple & Efficient Attention Networks](https://mlsanity.com/paper/2207.05844/) (2022)
- [MultiPath++: Efficient Information Fusion and Trajectory Aggregation for Behavior Prediction](https://mlsanity.com/paper/2111.14973/) (2021)
- [End-to-end Interpretable Neural Motion Planner](https://mlsanity.com/paper/2101.06679/) (2021)
- [Diffusion Probabilistic Modeling for Video Generation](https://mlsanity.com/paper/2203.09481/) (2022)
- [MP3: A Unified Model to Map, Perceive, Predict and Plan](https://mlsanity.com/paper/2101.06806/) (2021)
- [Guided Conditional Diffusion for Controllable Traffic Simulation](https://mlsanity.com/paper/2210.17366/) (2022)
- [Stochastic Trajectory Prediction via Motion Indeterminacy Diffusion](https://mlsanity.com/paper/2203.13777/) (2022)

## Built on by (most cited first, 30 of 213)

- [DiffusionDrive: Truncated Diffusion Model for End-to-End Autonomous Driving](https://mlsanity.com/paper/2411.15139/) (2024)
- [Understanding World or Predicting Future? A Comprehensive Survey of World Models](https://mlsanity.com/paper/2411.14499/) (2024)
- [Alpamayo-R1: Bridging Reasoning and Action Prediction for Generalizable Autonomous Driving in the Long Tail](https://mlsanity.com/paper/2511.00088/) (2025)
- [Diffusion-Based Planning for Autonomous Driving with Flexible Guidance](https://mlsanity.com/paper/2501.15564/) (2025)
- [GoalFlow: Goal-Driven Flow Matching for Multimodal Trajectories Generation in End-to-End Autonomous Driving](https://mlsanity.com/paper/2503.05689/) (2025)
- [Language-Guided Traffic Simulation via Scene-Level Diffusion](https://mlsanity.com/paper/2306.06344/) (2023)
- [Diffusion Models for Reinforcement Learning: A Survey](https://mlsanity.com/paper/2311.01223/) (2023)
- [Large Motion Model for Unified Multi-Modal Motion Generation](https://mlsanity.com/paper/2404.01284/) (2024)
- [DiffCast: A Unified Framework via Residual Diffusion for Precipitation Nowcasting](https://mlsanity.com/paper/2312.06734/) (2023)
- [UniTraj: A Unified Framework for Scalable Vehicle Trajectory Prediction](https://mlsanity.com/paper/2403.15098/) (2024)
- [SceneDiffuser: Efficient and Controllable Driving Simulation Initialization and Rollout](https://mlsanity.com/paper/2412.12129/) (2024)
- [DTPP: Differentiable Joint Conditional Prediction and Cost Evaluation for Tree Policy Planning in Autonomous Driving](https://mlsanity.com/paper/2310.05885/) (2023)
- [DiffuserLite: Towards Real-time Diffusion Planning](https://mlsanity.com/paper/2401.15443/) (2024)
- [Diffusion-ES: Gradient-free Planning with Diffusion for Autonomous Driving and Zero-Shot Instruction Following](https://mlsanity.com/paper/2402.06559/) (2024)
- [Gen-Drive: Enhancing Diffusion Generative Driving Policies with Reward Modeling and Reinforcement Learning Fine-tuning](https://mlsanity.com/paper/2410.05582/) (2024)
- [Closed-Loop Supervised Fine-Tuning of Tokenized Traffic Models](https://mlsanity.com/paper/2412.05334/) (2024)
- [Hydra-NeXt: Robust Closed-Loop Driving with Open-Loop Training](https://mlsanity.com/paper/2503.12030/) (2025)
- [Multi-Robot Motion Planning with Diffusion Models](https://mlsanity.com/paper/2410.03072/) (2024)
- [SingularTrajectory: Universal Trajectory Predictor Using Diffusion Model](https://mlsanity.com/paper/2403.18452/) (2024)
- [Deep Generative Models in Robotics: A Survey on Learning from Multimodal Demonstrations](https://mlsanity.com/paper/2408.04380/) (2024)
- [CarPlanner: Consistent Auto-regressive Trajectory Planning for Large-scale Reinforcement Learning in Autonomous Driving](https://mlsanity.com/paper/2502.19908/) (2025)
- [Model-Based Diffusion for Trajectory Optimization](https://mlsanity.com/paper/2407.01573/) (2024)
- [Variational Diffusion Posterior Sampling with Midpoint Guidance](https://mlsanity.com/paper/2410.09945/) (2024)
- [Can Language Beat Numerical Regression? Language-Based Multimodal Trajectory Prediction](https://mlsanity.com/paper/2403.18447/) (2024)
- [MoFlow: One-Step Flow Matching for Human Trajectory Forecasting via Implicit Maximum Likelihood Estimation based Distillation](https://mlsanity.com/paper/2503.09950/) (2025)
- [Multi-agent Long-term 3D Human Pose Forecasting via Interaction-aware Trajectory Conditioning](https://mlsanity.com/paper/2404.05218/) (2024)
- [The Integration of Prediction and Planning in Deep Learning Automated Driving Systems: A Review](https://mlsanity.com/paper/2308.05731/) (2023)
- [Towards Knowledge-driven Autonomous Driving](https://mlsanity.com/paper/2312.04316/) (2023)
- [DriveGPT: Scaling Autoregressive Behavior Models for Driving](https://mlsanity.com/paper/2412.14415/) (2024)
- [Scenario Dreamer: Vectorized Latent Diffusion for Generating Driving Simulation Environments](https://mlsanity.com/paper/2503.22496/) (2025)

## Abstract (arXiv)

We present MotionDiffuser, a diffusion based representation for the joint distribution of future trajectories over multiple agents. Such representation has several key advantages: first, our model learns a highly multimodal distribution that captures diverse future outcomes. Second, the simple predictor design requires only a single L2 loss training objective, and does not depend on trajectory anchors. Third, our model is capable of learning the joint distribution for the motion of multiple agents in a permutation-invariant manner. Furthermore, we utilize a compressed trajectory representation via PCA, which improves model performance and allows for efficient computation of the exact sample log probability. Subsequently, we propose a general constrained sampling framework that enables controlled trajectory sampling based on differentiable cost functions. This strategy enables a host of applications such as enforcing rules and physical priors, or creating tailored simulation scenarios. MotionDiffuser can be combined with existing backbone architectures to achieve top motion forecasting results. We obtain state-of-the-art results for multi-agent motion prediction on the Waymo Open Motion Dataset.