# Likelihood-Based Diverse Sampling for Trajectory Forecasting

arXiv: https://arxiv.org/abs/2011.15084 · HTML: https://mlsanity.com/paper/2011.15084/

## Key facts

- Cited by 16 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 30 Nov 2020.

## Built on by (most cited first, 16 of 16)

- [Generating Useful Accident-Prone Driving Scenarios via a Learned Traffic Prior](https://mlsanity.com/paper/2112.05077/) (2021)
- [Leveraging Future Relationship Reasoning for Vehicle Trajectory Prediction](https://mlsanity.com/paper/2305.14715/) (2023)
- [GATraj: A Graph- and Attention-based Multi-Agent Trajectory Prediction Model](https://mlsanity.com/paper/2209.07857/) (2022)
- [PreTraM: Self-Supervised Pre-training via Connecting Trajectory and Map](https://mlsanity.com/paper/2204.10435/) (2022)
- [LatentFormer: Multi-Agent Transformer-Based Interaction Modeling and Trajectory Prediction](https://mlsanity.com/paper/2203.01880/) (2022)
- [Unsupervised Sampling Promoting for Stochastic Human Trajectory Prediction](https://mlsanity.com/paper/2304.04298/) (2023)
- [Trajectory Prediction for Autonomous Driving: Progress, Limitations, and Future Directions](https://mlsanity.com/paper/2503.03262/) (2025)
- [NEST: A Neuromodulated Small-world Hypergraph Trajectory Prediction Model for Autonomous Driving](https://mlsanity.com/paper/2412.11682/) (2024)
- [Vision-based Multi-future Trajectory Prediction: A Survey](https://mlsanity.com/paper/2302.10463/) (2023)
- [CRITERIA: a New Benchmarking Paradigm for Evaluating Trajectory Prediction Models for Autonomous Driving](https://mlsanity.com/paper/2310.07794/) (2023)
- [Learning Disentangled Representations for Controllable Human Motion Prediction](https://mlsanity.com/paper/2207.01388/) (2022)
- [Enhancing Mapless Trajectory Prediction through Knowledge Distillation](https://mlsanity.com/paper/2306.14177/) (2023)
- [Unified Simulation, Perception, and Generation of Human Behavior](https://mlsanity.com/paper/2204.13678/) (2022)
- [Likely, Light, and Accurate Context-Free Clusters-based Trajectory Prediction](https://mlsanity.com/paper/2307.14788/) (2023)
- [LAMP: Lane-Aligned Motion Primitives for Feasible Trajectory Prediction](https://mlsanity.com/paper/2606.26661/) (2026)
- [Destination Support Restoration for Finite-Set Multimodal Trajectory Prediction](https://mlsanity.com/paper/2609.25942/) (2026)

## Abstract (arXiv)

Forecasting complex vehicle and pedestrian multi-modal distributions requires powerful probabilistic approaches. Normalizing flows (NF) have recently emerged as an attractive tool to model such distributions. However, a key drawback is that independent samples drawn from a flow model often do not adequately capture all the modes in the underlying distribution. We propose Likelihood-Based Diverse Sampling (LDS), a method for improving the quality and the diversity of trajectory samples from a pre-trained flow model. Rather than producing individual samples, LDS produces a set of trajectories in one shot. Given a pre-trained forecasting flow model, we train LDS using gradients from the model, to optimize an objective function that rewards high likelihood for individual trajectories in the predicted set, together with high spatial separation among trajectories. LDS outperforms state-of-art post-hoc neural diverse forecasting methods for various pre-trained flow models as well as conditional variational autoencoder (CVAE) models. Crucially, it can also be used for transductive trajectory forecasting, where the diverse forecasts are trained on-the-fly on unlabeled test examples. LDS is easy to implement, and we show that it offers a simple plug-in improvement over baselines on two challenging benchmarks. Code is at: https://github.com/JasonMa2016/LDS