# Stochastic Trajectory Prediction via Motion Indeterminacy Diffusion

arXiv: https://arxiv.org/abs/2203.13777 · HTML: https://mlsanity.com/paper/2203.13777/

## Key facts

- Cited by 185 papers in the map (data through 14 Oct 2026).
- Builds on 43 of its 55 references that are in the map.
- First posted on arXiv 25 Mar 2022.

## Builds on (most cited first, 30 of 43)

- [Denoising Diffusion Probabilistic Models](https://mlsanity.com/paper/2006.11239/) (2020)
- [U-Net: Convolutional Networks for Biomedical Image Segmentation](https://mlsanity.com/paper/1505.04597/) (2015)
- [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)
- [Generative Adversarial Networks](https://mlsanity.com/paper/2203.00667/) (2022)
- [Improved Denoising Diffusion Probabilistic Models](https://mlsanity.com/paper/2102.09672/) (2021)
- [DiffWave: A Versatile Diffusion Model for Audio Synthesis](https://mlsanity.com/paper/2009.09761/) (2020)
- [Diffusion Probabilistic Models for 3D Point Cloud Generation](https://mlsanity.com/paper/2103.01458/) (2021)
- [Social GAN: Socially Acceptable Trajectories with Generative Adversarial Networks](https://mlsanity.com/paper/1803.10892/) (2018)
- [ILVR: Conditioning Method for Denoising Diffusion Probabilistic Models](https://mlsanity.com/paper/2108.02938/) (2021)
- [WaveGrad: Estimating Gradients for Waveform Generation](https://mlsanity.com/paper/2009.00713/) (2020)
- [3D Shape Generation and Completion through Point-Voxel Diffusion](https://mlsanity.com/paper/2104.03670/) (2021)
- [Grad-TTS: A Diffusion Probabilistic Model for Text-to-Speech](https://mlsanity.com/paper/2105.06337/) (2021)
- [TNT: Target-driveN Trajectory Prediction](https://mlsanity.com/paper/2008.08294/) (2020)
- [Social-STGCNN: A Social Spatio-Temporal Graph Convolutional Neural Network for Human Trajectory Prediction](https://mlsanity.com/paper/2002.11927/) (2020)
- [DESIRE: Distant Future Prediction in Dynamic Scenes with Interacting Agents](https://mlsanity.com/paper/1704.04394/) (2017)
- [SoPhie: An Attentive GAN for Predicting Paths Compliant to Social and Physical Constraints](https://mlsanity.com/paper/1806.01482/) (2018)
- [It Is Not the Journey but the Destination: Endpoint Conditioned Trajectory Prediction](https://mlsanity.com/paper/2004.02025/) (2020)
- [Social-BiGAT: Multimodal Trajectory Forecasting using Bicycle-GAN and Graph Attention Networks](https://mlsanity.com/paper/1907.03395/) (2019)
- [Gotta Go Fast When Generating Data with Score-Based Models](https://mlsanity.com/paper/2105.14080/) (2021)
- [Spatio-Temporal Graph Transformer Networks for Pedestrian Trajectory Prediction](https://mlsanity.com/paper/2005.08514/) (2020)
- [Social Attention: Modeling Attention in Human Crowds](https://mlsanity.com/paper/1710.04689/) (2017)
- [Multiple Futures Prediction](https://mlsanity.com/paper/1911.00997/) (2019)
- [From Goals, Waypoints & Paths To Long Term Human Trajectory Forecasting](https://mlsanity.com/paper/2012.01526/) (2020)
- [Multi-Agent Tensor Fusion for Contextual Trajectory Prediction](https://mlsanity.com/paper/1904.04776/) (2019)
- [Learning to Efficiently Sample from Diffusion Probabilistic Models](https://mlsanity.com/paper/2106.03802/) (2021)
- [SR-LSTM: State Refinement for LSTM towards Pedestrian Trajectory Prediction](https://mlsanity.com/paper/1903.02793/) (2019)
- [Noise Estimation for Generative Diffusion Models](https://mlsanity.com/paper/2104.02600/) (2021)
- [TPNet: Trajectory Proposal Network for Motion Prediction](https://mlsanity.com/paper/2004.12255/) (2020)

## Built on by (most cited first, 30 of 185)

- [MotionDiffuser: Controllable Multi-Agent Motion Prediction using Diffusion](https://mlsanity.com/paper/2306.03083/) (2023)
- [Guided Conditional Diffusion for Controllable Traffic Simulation](https://mlsanity.com/paper/2210.17366/) (2022)
- [Trace and Pace: Controllable Pedestrian Animation via Guided Trajectory Diffusion](https://mlsanity.com/paper/2304.01893/) (2023)
- [Leapfrog Diffusion Model for Stochastic Trajectory Prediction](https://mlsanity.com/paper/2303.10895/) (2023)
- [Language-Guided Traffic Simulation via Scene-Level Diffusion](https://mlsanity.com/paper/2306.06344/) (2023)
- [DiffPose: Toward More Reliable 3D Pose Estimation](https://mlsanity.com/paper/2211.16940/) (2022)
- [EqMotion: Equivariant Multi-agent Motion Prediction with Invariant Interaction Reasoning](https://mlsanity.com/paper/2303.10876/) (2023)
- [BeLFusion: Latent Diffusion for Behavior-Driven Human Motion Prediction](https://mlsanity.com/paper/2211.14304/) (2022)
- [Spatio-temporal Diffusion Point Processes](https://mlsanity.com/paper/2305.12403/) (2023)
- [Learning Pedestrian Group Representations for Multi-modal Trajectory Prediction](https://mlsanity.com/paper/2207.09953/) (2022)
- [EigenTrajectory: Low-Rank Descriptors for Multi-Modal Trajectory Forecasting](https://mlsanity.com/paper/2307.09306/) (2023)
- [SAFE-SIM: Safety-Critical Closed-Loop Traffic Simulation with Diffusion-Controllable Adversaries](https://mlsanity.com/paper/2401.00391/) (2023)
- [SingularTrajectory: Universal Trajectory Predictor Using Diffusion Model](https://mlsanity.com/paper/2403.18452/) (2024)
- [Social-Transmotion: Promptable Human Trajectory Prediction](https://mlsanity.com/paper/2312.16168/) (2023)
- [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)
- [Dynamic-Group-Aware Networks for Multi-Agent Trajectory Prediction with Relational Reasoning](https://mlsanity.com/paper/2206.13114/) (2022)
- [Human Joint Kinematics Diffusion-Refinement for Stochastic Motion Prediction](https://mlsanity.com/paper/2210.05976/) (2022)
- [Stochastic Multi-Person 3D Motion Forecasting](https://mlsanity.com/paper/2306.05421/) (2023)
- [Divide-and-Conquer Posterior Sampling for Denoising Diffusion Priors](https://mlsanity.com/paper/2403.11407/) (2024)
- [Fast Inference and Update of Probabilistic Density Estimation on Trajectory Prediction](https://mlsanity.com/paper/2308.08824/) (2023)
- [Diffusion-based Image Translation with Label Guidance for Domain Adaptive Semantic Segmentation](https://mlsanity.com/paper/2308.12350/) (2023)
- [Distribution-Aligned Diffusion for Human Mesh Recovery](https://mlsanity.com/paper/2308.13369/) (2023)
- [SocialCircle: Learning the Angle-based Social Interaction Representation for Pedestrian Trajectory Prediction](https://mlsanity.com/paper/2310.05370/) (2023)
- [GATraj: A Graph- and Attention-based Multi-Agent Trajectory Prediction Model](https://mlsanity.com/paper/2209.07857/) (2022)
- [LG-Traj: LLM Guided Pedestrian Trajectory Prediction](https://mlsanity.com/paper/2403.08032/) (2024)
- [SceneDM: Scene-level Multi-agent Trajectory Generation with Consistent Diffusion Models](https://mlsanity.com/paper/2311.15736/) (2023)
- [6D-Diff: A Keypoint Diffusion Framework for 6D Object Pose Estimation](https://mlsanity.com/paper/2401.00029/) (2023)
- [Adapting to Length Shift: FlexiLength Network for Trajectory Prediction](https://mlsanity.com/paper/2404.00742/) (2024)
- [EquiDiff: A Conditional Equivariant Diffusion Model For Trajectory Prediction](https://mlsanity.com/paper/2308.06564/) (2023)

## Abstract (arXiv)

Human behavior has the nature of indeterminacy, which requires the pedestrian trajectory prediction system to model the multi-modality of future motion states. Unlike existing stochastic trajectory prediction methods which usually use a latent variable to represent multi-modality, we explicitly simulate the process of human motion variation from indeterminate to determinate. In this paper, we present a new framework to formulate the trajectory prediction task as a reverse process of motion indeterminacy diffusion (MID), in which we progressively discard indeterminacy from all the walkable areas until reaching the desired trajectory. This process is learned with a parameterized Markov chain conditioned by the observed trajectories. We can adjust the length of the chain to control the degree of indeterminacy and balance the diversity and determinacy of the predictions. Specifically, we encode the history behavior information and the social interactions as a state embedding and devise a Transformer-based diffusion model to capture the temporal dependencies of trajectories. Extensive experiments on the human trajectory prediction benchmarks including the Stanford Drone and ETH/UCY datasets demonstrate the superiority of our method. Code is available at https://github.com/gutianpei/MID.