# EquiDiff: A Conditional Equivariant Diffusion Model For Trajectory Prediction

arXiv: https://arxiv.org/abs/2308.06564 · HTML: https://mlsanity.com/paper/2308.06564/

## Key facts

- Cited by 21 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 17 of its 22 references that are in the map.
- First posted on arXiv 12 Aug 2023.

## 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, 17 of 17)

- [Denoising Diffusion Probabilistic Models](https://mlsanity.com/paper/2006.11239/) (2020)
- [Graph Attention Networks](https://mlsanity.com/paper/1710.10903/) (2017)
- [Layer Normalization](https://mlsanity.com/paper/1607.06450/) (2016)
- [Generative Adversarial Networks](https://mlsanity.com/paper/2203.00667/) (2022)
- [Empirical Evaluation of Gated Recurrent Neural Networks on Sequence Modeling](https://mlsanity.com/paper/1412.3555/) (2014)
- [Social GAN: Socially Acceptable Trajectories with Generative Adversarial Networks](https://mlsanity.com/paper/1803.10892/) (2018)
- [Tutorial on Variational Autoencoders](https://mlsanity.com/paper/1606.05908/) (2016)
- [Autoregressive Denoising Diffusion Models for Multivariate Probabilistic Time Series Forecasting](https://mlsanity.com/paper/2101.12072/) (2021)
- [Vector Neurons: A General Framework for SO(3)-Equivariant Networks](https://mlsanity.com/paper/2104.12229/) (2021)
- [Convolutional Social Pooling for Vehicle Trajectory Prediction](https://mlsanity.com/paper/1805.06771/) (2018)
- [Stochastic Trajectory Prediction via Motion Indeterminacy Diffusion](https://mlsanity.com/paper/2203.13777/) (2022)
- [Multi-Agent Tensor Fusion for Contextual Trajectory Prediction](https://mlsanity.com/paper/1904.04776/) (2019)
- [EqMotion: Equivariant Multi-agent Motion Prediction with Invariant Interaction Reasoning](https://mlsanity.com/paper/2303.10876/) (2023)
- [Imitating Driver Behavior with Generative Adversarial Networks](https://mlsanity.com/paper/1701.06699/) (2017)
- [GRIP++: Enhanced Graph-based Interaction-aware Trajectory Prediction for Autonomous Driving](https://mlsanity.com/paper/1907.07792/) (2019)
- [Multimodal Deep Generative Models for Trajectory Prediction: A Conditional Variational Autoencoder Approach](https://mlsanity.com/paper/2008.03880/) (2020)
- [VN-Transformer: Rotation-Equivariant Attention for Vector Neurons](https://mlsanity.com/paper/2206.04176/) (2022)

## Built on by (most cited first, 21 of 21)

- [Diffusion Models for Reinforcement Learning: A Survey](https://mlsanity.com/paper/2311.01223/) (2023)
- [EquiBot: SIM(3)-Equivariant Diffusion Policy for Generalizable and Data Efficient Learning](https://mlsanity.com/paper/2407.01479/) (2024)
- [Equivariant Diffusion Policy](https://mlsanity.com/paper/2407.01812/) (2024)
- [Theia: Distilling Diverse Vision Foundation Models for Robot Learning](https://mlsanity.com/paper/2407.20179/) (2024)
- [Diffusion-Based Environment-Aware Trajectory Prediction](https://mlsanity.com/paper/2403.11643/) (2024)
- [Reliable Trajectory Prediction and Uncertainty Quantification with Conditioned Diffusion Models](https://mlsanity.com/paper/2405.14384/) (2024)
- [A Survey of Generative AI for Intelligent Transportation Systems: Road Transportation Perspective](https://mlsanity.com/paper/2312.08248/) (2023)
- [A Comprehensive Survey on Diffusion Models and Their Applications](https://mlsanity.com/paper/2408.10207/) (2024)
- [A Gentle Introduction and Tutorial on Deep Generative Models in Transportation Research](https://mlsanity.com/paper/2410.07066/) (2024)
- [Preferred-Action-Optimized Diffusion Policies for Offline Reinforcement Learning](https://mlsanity.com/paper/2405.18729/) (2024)
- [FollowGen: A Scaled Noise Conditional Diffusion Model for Car-Following Trajectory Prediction](https://mlsanity.com/paper/2411.16747/) (2024)
- [Zero-Shot Visual Generalization in Robot Manipulation](https://mlsanity.com/paper/2505.11719/) (2025)
- [EquiReg: Equivariance Regularized Diffusion for Inverse Problems](https://mlsanity.com/paper/2505.22973/) (2025)
- [Crossfusor: A Cross-Attention Transformer Enhanced Conditional Diffusion Model for Car-Following Trajectory Prediction](https://mlsanity.com/paper/2406.11941/) (2024)
- [Diffusion^2: Dual Diffusion Model with Uncertainty-Aware Adaptive Noise for Momentary Trajectory Prediction](https://mlsanity.com/paper/2510.04365/) (2025)
- [Occlusion-Aware Diffusion Model for Pedestrian Intention Prediction](https://mlsanity.com/paper/2511.00858/) (2025)
- [EquiDexFlow: Contact-Grounded SE(3)-Equivariant Dexterous Grasp Generative Flows](https://mlsanity.com/paper/2606.12728/) (2026)
- [Robust Planning for Autonomous Driving via Mixed Adversarial Diffusion Predictions](https://mlsanity.com/paper/2505.12327/) (2025)
- [SocialTraj: Two-Stage Socially-Aware Trajectory Prediction for Autonomous Driving via Conditional Diffusion Model](https://mlsanity.com/paper/2509.17850/) (2025)
- [Collaborative-Distilled Diffusion Models (CDDM) for Accelerated and Lightweight Trajectory Prediction](https://mlsanity.com/paper/2510.00627/) (2025)
- [From Camera-Based Sensing to Reasoning: A Comprehensive Review Toward Proactive Vulnerable Road User Safety](https://mlsanity.com/paper/2510.03314/) (2025)

## Abstract (arXiv)

Accurate trajectory prediction is crucial for the safe and efficient operation of autonomous vehicles. The growing popularity of deep learning has led to the development of numerous methods for trajectory prediction. While deterministic deep learning models have been widely used, deep generative models have gained popularity as they learn data distributions from training data and account for trajectory uncertainties. In this study, we propose EquiDiff, a deep generative model for predicting future vehicle trajectories. EquiDiff is based on the conditional diffusion model, which generates future trajectories by incorporating historical information and random Gaussian noise. The backbone model of EquiDiff is an SO(2)-equivariant transformer that fully utilizes the geometric properties of location coordinates. In addition, we employ Recurrent Neural Networks and Graph Attention Networks to extract social interactions from historical trajectories. To evaluate the performance of EquiDiff, we conduct extensive experiments on the NGSIM dataset. Our results demonstrate that EquiDiff outperforms other baseline models in short-term prediction, but has slightly higher errors for long-term prediction. Furthermore, we conduct an ablation study to investigate the contribution of each component of EquiDiff to the prediction accuracy. Additionally, we present a visualization of the generation process of our diffusion model, providing insights into the uncertainty of the prediction.