# Diverse Trajectory Forecasting with Determinantal Point Processes

arXiv: https://arxiv.org/abs/1907.04967 · HTML: https://mlsanity.com/paper/1907.04967/

## Key facts

- Cited by 80 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 11 Jul 2019.

## Built on by (most cited first, 30 of 80)

- [AgentFormer: Agent-Aware Transformers for Socio-Temporal Multi-Agent Forecasting](https://mlsanity.com/paper/2103.14023/) (2021)
- [DenseTNT: End-to-end Trajectory Prediction from Dense Goal Sets](https://mlsanity.com/paper/2108.09640/) (2021)
- [MultiPath++: Efficient Information Fusion and Trajectory Aggregation for Behavior Prediction](https://mlsanity.com/paper/2111.14973/) (2021)
- [Stochastic Scene-Aware Motion Prediction](https://mlsanity.com/paper/2108.08284/) (2021)
- [TrafficSim: Learning to Simulate Realistic Multi-Agent Behaviors](https://mlsanity.com/paper/2101.06557/) (2021)
- [InterDiff: Generating 3D Human-Object Interactions with Physics-Informed Diffusion](https://mlsanity.com/paper/2308.16905/) (2023)
- [GLAMR: Global Occlusion-Aware Human Mesh Recovery with Dynamic Cameras](https://mlsanity.com/paper/2112.01524/) (2021)
- [ViP3D: End-to-end Visual Trajectory Prediction via 3D Agent Queries](https://mlsanity.com/paper/2208.01582/) (2022)
- [LookOut: Diverse Multi-Future Prediction and Planning for Self-Driving](https://mlsanity.com/paper/2101.06547/) (2021)
- [BeLFusion: Latent Diffusion for Behavior-Driven Human Motion Prediction](https://mlsanity.com/paper/2211.14304/) (2022)
- [M2I: From Factored Marginal Trajectory Prediction to Interactive Prediction](https://mlsanity.com/paper/2202.11884/) (2022)
- [HumanMAC: Masked Motion Completion for Human Motion Prediction](https://mlsanity.com/paper/2302.03665/) (2023)
- [Generating Smooth Pose Sequences for Diverse Human Motion Prediction](https://mlsanity.com/paper/2108.08422/) (2021)
- [LaPred: Lane-Aware Prediction of Multi-Modal Future Trajectories of Dynamic Agents](https://mlsanity.com/paper/2104.00249/) (2021)
- [ScePT: Scene-consistent, Policy-based Trajectory Predictions for Planning](https://mlsanity.com/paper/2206.13387/) (2022)
- [Multi-Person 3D Motion Prediction with Multi-Range Transformers](https://mlsanity.com/paper/2111.12073/) (2021)
- [JFP: Joint Future Prediction with Interactive Multi-Agent Modeling for Autonomous Driving](https://mlsanity.com/paper/2212.08710/) (2022)
- [Divide-and-Conquer for Lane-Aware Diverse Trajectory Prediction](https://mlsanity.com/paper/2104.08277/) (2021)
- [Graph-based Spatial Transformer with Memory Replay for Multi-future Pedestrian Trajectory Prediction](https://mlsanity.com/paper/2206.05712/) (2022)
- [Diverse Human Motion Prediction Guided by Multi-Level Spatial-Temporal Anchors](https://mlsanity.com/paper/2302.04860/) (2023)
- [PACE: Human and Camera Motion Estimation from in-the-wild Videos](https://mlsanity.com/paper/2310.13768/) (2023)
- [A generic diffusion-based approach for 3D human pose prediction in the wild](https://mlsanity.com/paper/2210.05669/) (2022)
- [Diverse Human Motion Prediction via Gumbel-Softmax Sampling from an Auxiliary Space](https://mlsanity.com/paper/2207.07351/) (2022)
- [MoFlow: One-Step Flow Matching for Human Trajectory Forecasting via Implicit Maximum Likelihood Estimation based Distillation](https://mlsanity.com/paper/2503.09950/) (2025)
- [Motron: Multimodal Probabilistic Human Motion Forecasting](https://mlsanity.com/paper/2203.04132/) (2022)
- [An information-theoretic perspective on intrinsic motivation in reinforcement learning: a survey](https://mlsanity.com/paper/2209.08890/) (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)
- [Aggregated Multi-GANs for Controlled 3D Human Motion Prediction](https://mlsanity.com/paper/2103.09755/) (2021)
- [TrajGen: Generating Realistic and Diverse Trajectories with Reactive and Feasible Agent Behaviors for Autonomous Driving](https://mlsanity.com/paper/2203.16792/) (2022)

## Abstract (arXiv)

The ability to forecast a set of likely yet diverse possible future behaviors of an agent (e.g., future trajectories of a pedestrian) is essential for safety-critical perception systems (e.g., autonomous vehicles). In particular, a set of possible future behaviors generated by the system must be diverse to account for all possible outcomes in order to take necessary safety precautions. It is not sufficient to maintain a set of the most likely future outcomes because the set may only contain perturbations of a single outcome. While generative models such as variational autoencoders (VAEs) have been shown to be a powerful tool for learning a distribution over future trajectories, randomly drawn samples from the learned implicit likelihood model may not be diverse -- the likelihood model is derived from the training data distribution and the samples will concentrate around the major mode that has most data. In this work, we propose to learn a diversity sampling function (DSF) that generates a diverse and likely set of future trajectories. The DSF maps forecasting context features to a set of latent codes which can be decoded by a generative model (e.g., VAE) into a set of diverse trajectory samples. Concretely, the process of identifying the diverse set of samples is posed as a parameter estimation of the DSF. To learn the parameters of the DSF, the diversity of the trajectory samples is evaluated by a diversity loss based on a determinantal point process (DPP). Gradient descent is performed over the DSF parameters, which in turn move the latent codes of the sample set to find an optimal diverse and likely set of trajectories. Our method is a novel application of DPPs to optimize a set of items (trajectories) in continuous space. We demonstrate the diversity of the trajectories produced by our approach on both low-dimensional 2D trajectory data and high-dimensional human motion data.