# Non-Probability Sampling Network for Stochastic Human Trajectory Prediction

arXiv: https://arxiv.org/abs/2203.13471 · HTML: https://mlsanity.com/paper/2203.13471/

## Key facts

- Cited by 46 papers in the map (data through 14 Oct 2026).
- Builds on 31 of its 67 references that are in the map.
- First posted on arXiv 25 Mar 2022.

## Builds on (most cited first, 30 of 31)

- [Semi-Supervised Classification with Graph Convolutional Networks](https://mlsanity.com/paper/1609.02907/) (2016)
- [Graph Attention Networks](https://mlsanity.com/paper/1710.10903/) (2017)
- [A Style-Based Generator Architecture for Generative Adversarial Networks](https://mlsanity.com/paper/1812.04948/) (2018)
- [InfoGAN: Interpretable Representation Learning by Information Maximizing Generative Adversarial Nets](https://mlsanity.com/paper/1606.03657/) (2016)
- [Social GAN: Socially Acceptable Trajectories with Generative Adversarial Networks](https://mlsanity.com/paper/1803.10892/) (2018)
- [TNT: Target-driveN Trajectory Prediction](https://mlsanity.com/paper/2008.08294/) (2020)
- [AgentFormer: Agent-Aware Transformers for Socio-Temporal Multi-Agent Forecasting](https://mlsanity.com/paper/2103.14023/) (2021)
- [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)
- [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)
- [Multi-Agent Tensor Fusion for Contextual Trajectory Prediction](https://mlsanity.com/paper/1904.04776/) (2019)
- [Peeking into the Future: Predicting Future Person Activities and Locations in Videos](https://mlsanity.com/paper/1902.03748/) (2019)
- [SR-LSTM: State Refinement for LSTM towards Pedestrian Trajectory Prediction](https://mlsanity.com/paper/1903.02793/) (2019)
- [Learning in an Uncertain World: Representing Ambiguity Through Multiple Hypotheses](https://mlsanity.com/paper/1612.00197/) (2016)
- [SGCN:Sparse Graph Convolution Network for Pedestrian Trajectory Prediction](https://mlsanity.com/paper/2104.01528/) (2021)
- [ChamNet: Towards Efficient Network Design through Platform-Aware Model Adaptation](https://mlsanity.com/paper/1812.08934/) (2018)
- [Conditional Generative Neural System for Probabilistic Trajectory Prediction](https://mlsanity.com/paper/1905.01631/) (2019)
- [The Garden of Forking Paths: Towards Multi-Future Trajectory Prediction](https://mlsanity.com/paper/1912.06445/) (2019)
- [MANTRA: Memory Augmented Networks for Multiple Trajectory Prediction](https://mlsanity.com/paper/2006.03340/) (2020)
- [Recursive Social Behavior Graph for Trajectory Prediction](https://mlsanity.com/paper/2004.10402/) (2020)
- [MG-GAN: A Multi-Generator Model Preventing Out-of-Distribution Samples in Pedestrian Trajectory Prediction](https://mlsanity.com/paper/2108.09274/) (2021)
- [Social NCE: Contrastive Learning of Socially-aware Motion Representations](https://mlsanity.com/paper/2012.11717/) (2020)
- [Human Trajectory Prediction via Counterfactual Analysis](https://mlsanity.com/paper/2107.14202/) (2021)
- [Reciprocal Learning Networks for Human Trajectory Prediction](https://mlsanity.com/paper/2004.04340/) (2020)
- [Ladybird: Quasi-Monte Carlo Sampling for Deep Implicit Field Based 3D Reconstruction with Symmetry](https://mlsanity.com/paper/2007.13393/) (2020)
- [Dynamic and Static Context-aware LSTM for Multi-agent Motion Prediction](https://mlsanity.com/paper/2008.00777/) (2020)

## Built on by (most cited first, 30 of 46)

- [Leapfrog Diffusion Model for Stochastic Trajectory Prediction](https://mlsanity.com/paper/2303.10895/) (2023)
- [Leveraging Future Relationship Reasoning for Vehicle Trajectory Prediction](https://mlsanity.com/paper/2305.14715/) (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)
- [SingularTrajectory: Universal Trajectory Predictor Using Diffusion Model](https://mlsanity.com/paper/2403.18452/) (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)
- [Dynamic-Group-Aware Networks for Multi-Agent Trajectory Prediction with Relational Reasoning](https://mlsanity.com/paper/2206.13114/) (2022)
- [LG-Traj: LLM Guided Pedestrian Trajectory Prediction](https://mlsanity.com/paper/2403.08032/) (2024)
- [MART: MultiscAle Relational Transformer Networks for Multi-agent Trajectory Prediction](https://mlsanity.com/paper/2407.21635/) (2024)
- [Multi-Transmotion: Pre-trained Model for Human Motion Prediction](https://mlsanity.com/paper/2411.02673/) (2024)
- [T4P: Test-Time Training of Trajectory Prediction via Masked Autoencoder and Actor-specific Token Memory](https://mlsanity.com/paper/2403.10052/) (2024)
- [Unsupervised Sampling Promoting for Stochastic Human Trajectory Prediction](https://mlsanity.com/paper/2304.04298/) (2023)
- [Progressive Pretext Task Learning for Human Trajectory Prediction](https://mlsanity.com/paper/2407.11588/) (2024)
- [Unified Uncertainty-Aware Diffusion for Multi-Agent Trajectory Modeling](https://mlsanity.com/paper/2503.18589/) (2025)
- [Trajectory Prediction for Autonomous Driving: Progress, Limitations, and Future Directions](https://mlsanity.com/paper/2503.03262/) (2025)
- [Collaborative Uncertainty Benefits Multi-Agent Multi-Modal Trajectory Forecasting](https://mlsanity.com/paper/2207.05195/) (2022)
- [Improving Transferability for Cross-domain Trajectory Prediction via Neural Stochastic Differential Equation](https://mlsanity.com/paper/2312.15906/) (2023)
- [Intention-aware Denoising Diffusion Model for Trajectory Prediction](https://mlsanity.com/paper/2403.09190/) (2024)
- [Recurrent Aligned Network for Generalized Pedestrian Trajectory Prediction](https://mlsanity.com/paper/2403.05810/) (2024)
- [MATRIX: Multi-Agent Trajectory Generation with Diverse Contexts](https://mlsanity.com/paper/2403.06041/) (2024)
- [Vision-based Multi-future Trajectory Prediction: A Survey](https://mlsanity.com/paper/2302.10463/) (2023)
- [TrajPAC: Towards Robustness Verification of Pedestrian Trajectory Prediction Models](https://mlsanity.com/paper/2308.05985/) (2023)
- [CRITERIA: a New Benchmarking Paradigm for Evaluating Trajectory Prediction Models for Autonomous Driving](https://mlsanity.com/paper/2310.07794/) (2023)
- [Continuous Locomotive Crowd Behavior Generation](https://mlsanity.com/paper/2504.04756/) (2025)
- [AMD: Adaptive Momentum and Decoupled Contrastive Learning Framework for Robust Long-Tail Trajectory Prediction](https://mlsanity.com/paper/2507.01801/) (2025)
- [ViTE: Virtual Graph Trajectory Expert Router for Pedestrian Trajectory Prediction](https://mlsanity.com/paper/2511.12214/) (2025)
- [Sparse Pedestrian Character Learning for Trajectory Prediction](https://mlsanity.com/paper/2311.15512/) (2023)
- [Evaluating Human Trajectory Prediction with Metamorphic Testing](https://mlsanity.com/paper/2407.18756/) (2024)
- [OmniTraj: Pre-Training on Heterogeneous Data for Adaptive and Zero-Shot Human Trajectory Prediction](https://mlsanity.com/paper/2507.23657/) (2025)

## Abstract (arXiv)

Capturing multimodal natures is essential for stochastic pedestrian trajectory prediction, to infer a finite set of future trajectories. The inferred trajectories are based on observation paths and the latent vectors of potential decisions of pedestrians in the inference step. However, stochastic approaches provide varying results for the same data and parameter settings, due to the random sampling of the latent vector. In this paper, we analyze the problem by reconstructing and comparing probabilistic distributions from prediction samples and socially-acceptable paths, respectively. Through this analysis, we observe that the inferences of all stochastic models are biased toward the random sampling, and fail to generate a set of realistic paths from finite samples. The problem cannot be resolved unless an infinite number of samples is available, which is infeasible in practice. We introduce that the Quasi-Monte Carlo (QMC) method, ensuring uniform coverage on the sampling space, as an alternative to the conventional random sampling. With the same finite number of samples, the QMC improves all the multimodal prediction results. We take an additional step ahead by incorporating a learnable sampling network into the existing networks for trajectory prediction. For this purpose, we propose the Non-Probability Sampling Network (NPSN), a very small network (~5K parameters) that generates purposive sample sequences using the past paths of pedestrians and their social interactions. Extensive experiments confirm that NPSN can significantly improve both the prediction accuracy (up to 60%) and reliability of the public pedestrian trajectory prediction benchmark. Code is publicly available at https://github.com/inhwanbae/NPSN .