# Stochastic Trajectory Prediction under Unstructured Constraints

arXiv: https://arxiv.org/abs/2503.14203 · HTML: https://mlsanity.com/paper/2503.14203/

## Key facts

- Cited by 3 papers in the map (data through 14 Oct 2026).
- Builds on 27 of its 42 references that are in the map.
- First posted on arXiv 18 Mar 2025.

## Builds on (most cited first, 27 of 27)

- [Denoising Diffusion Probabilistic Models](https://mlsanity.com/paper/2006.11239/) (2020)
- [Adding Conditional Control to Text-to-Image Diffusion Models](https://mlsanity.com/paper/2302.05543/) (2023)
- [Learning to summarize from human feedback](https://mlsanity.com/paper/2009.01325/) (2020)
- [Conditional Generative Adversarial Nets](https://mlsanity.com/paper/1411.1784/) (2014)
- [Social GAN: Socially Acceptable Trajectories with Generative Adversarial Networks](https://mlsanity.com/paper/1803.10892/) (2018)
- [Is Conditional Generative Modeling all you need for Decision-Making?](https://mlsanity.com/paper/2211.15657/) (2022)
- [A Recurrent Latent Variable Model for Sequential Data](https://mlsanity.com/paper/1506.02216/) (2015)
- [Understanding Diffusion Models: A Unified Perspective](https://mlsanity.com/paper/2208.11970/) (2022)
- [Social-STGCNN: A Social Spatio-Temporal Graph Convolutional Neural Network for Human Trajectory Prediction](https://mlsanity.com/paper/2002.11927/) (2020)
- [SoPhie: An Attentive GAN for Predicting Paths Compliant to Social and Physical Constraints](https://mlsanity.com/paper/1806.01482/) (2018)
- [Principled Reinforcement Learning with Human Feedback from Pairwise or K-wise Comparisons](https://mlsanity.com/paper/2301.11270/) (2023)
- [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)
- [A Survey of Human-in-the-loop for Machine Learning](https://mlsanity.com/paper/2108.00941/) (2021)
- [Stochastic Trajectory Prediction via Motion Indeterminacy Diffusion](https://mlsanity.com/paper/2203.13777/) (2022)
- [From Goals, Waypoints & Paths To Long Term Human Trajectory Forecasting](https://mlsanity.com/paper/2012.01526/) (2020)
- [GAN-Control: Explicitly Controllable GANs](https://mlsanity.com/paper/2101.02477/) (2021)
- [Conditional Generative Neural System for Probabilistic Trajectory Prediction](https://mlsanity.com/paper/1905.01631/) (2019)
- [MG-GAN: A Multi-Generator Model Preventing Out-of-Distribution Samples in Pedestrian Trajectory Prediction](https://mlsanity.com/paper/2108.09274/) (2021)
- [Trajectory Prediction with Latent Belief Energy-Based Model](https://mlsanity.com/paper/2104.03086/) (2021)
- [Three Steps to Multimodal Trajectory Prediction: Modality Clustering, Classification and Synthesis](https://mlsanity.com/paper/2103.07854/) (2021)
- [Human Trajectory Prediction via Counterfactual Analysis](https://mlsanity.com/paper/2107.14202/) (2021)
- [Shared Cross-Modal Trajectory Prediction for Autonomous Driving](https://mlsanity.com/paper/2011.08436/) (2020)
- [Accelerating Human-in-the-loop Machine Learning: Challenges and Opportunities](https://mlsanity.com/paper/1804.05892/) (2018)
- [Stochastic trajectory prediction with social graph network](https://mlsanity.com/paper/1907.10233/) (2019)
- [Probabilistic Trajectory Prediction with Structural Constraints](https://mlsanity.com/paper/2107.04193/) (2021)

## Built on by (most cited first, 3 of 3)

- [Recent Advances in Multi-Agent Human Trajectory Prediction: A Comprehensive Review](https://mlsanity.com/paper/2506.14831/) (2025)
- [Eye Gaze-Informed and Context-Aware Pedestrian Trajectory Prediction in Shared Spaces with Automated Shuttles: A Virtual Reality Study](https://mlsanity.com/paper/2603.19812/) (2026)
- [Uncertainty-Aware Diffusion Model for Multimodal Highway Trajectory Prediction via DDIM Sampling](https://mlsanity.com/paper/2602.21319/) (2026)

## Abstract (arXiv)

Trajectory prediction facilitates effective planning and decision-making, while constrained trajectory prediction integrates regulation into prediction. Recent advances in constrained trajectory prediction focus on structured constraints by constructing optimization objectives. However, handling unstructured constraints is challenging due to the lack of differentiable formal definitions. To address this, we propose a novel method for constrained trajectory prediction using a conditional generative paradigm, named Controllable Trajectory Diffusion (CTD). The key idea is that any trajectory corresponds to a degree of conformity to a constraint. By quantifying this degree and treating it as a condition, a model can implicitly learn to predict trajectories under unstructured constraints. CTD employs a pre-trained scoring model to predict the degree of conformity (i.e., a score), and uses this score as a condition for a conditional diffusion model to generate trajectories. Experimental results demonstrate that CTD achieves high accuracy on the ETH/UCY and SDD benchmarks. Qualitative analysis confirms that CTD ensures adherence to unstructured constraints and can predict trajectories that satisfy combinatorial constraints.