# JointDiff: Bridging Continuous and Discrete in Multi-Agent Trajectory Generation

arXiv: https://arxiv.org/abs/2509.22522 · HTML: https://mlsanity.com/paper/2509.22522/

## Key facts

- Cited by 5 papers in the map (data through 14 Oct 2026).
- Builds on 55 of its 69 references that are in the map.
- First posted on arXiv 26 Sep 2025.

## Builds on (most cited first, 30 of 55)

- [Attention Is All You Need](https://mlsanity.com/paper/1706.03762/) (2017)
- [Denoising Diffusion Probabilistic Models](https://mlsanity.com/paper/2006.11239/) (2020)
- [High-Resolution Image Synthesis with Latent Diffusion Models](https://mlsanity.com/paper/2112.10752/) (2021)
- [Exploring the Limits of Transfer Learning with a Unified Text-to-Text Transformer](https://mlsanity.com/paper/1910.10683/) (2019)
- [Denoising Diffusion Implicit Models](https://mlsanity.com/paper/2010.02502/) (2020)
- [Diffusion Models Beat GANs on Image Synthesis](https://mlsanity.com/paper/2105.05233/) (2021)
- [Classifier-Free Diffusion Guidance](https://mlsanity.com/paper/2207.12598/) (2022)
- [Mamba: Linear-Time Sequence Modeling with Selective State Spaces](https://mlsanity.com/paper/2312.00752/) (2023)
- [Improved Denoising Diffusion Probabilistic Models](https://mlsanity.com/paper/2102.09672/) (2021)
- [Video Diffusion Models](https://mlsanity.com/paper/2204.03458/) (2022)
- [Structured Denoising Diffusion Models in Discrete State-Spaces](https://mlsanity.com/paper/2107.03006/) (2021)
- [Discrete Diffusion Modeling by Estimating the Ratios of the Data Distribution](https://mlsanity.com/paper/2310.16834/) (2023)
- [CSDI: Conditional Score-based Diffusion Models for Probabilistic Time Series Imputation](https://mlsanity.com/paper/2107.03502/) (2021)
- [Argmax Flows and Multinomial Diffusion: Learning Categorical Distributions](https://mlsanity.com/paper/2102.05379/) (2021)
- [Neural Relational Inference for Interacting Systems](https://mlsanity.com/paper/1802.04687/) (2018)
- [AgentFormer: Agent-Aware Transformers for Socio-Temporal Multi-Agent Forecasting](https://mlsanity.com/paper/2103.14023/) (2021)
- [SoPhie: An Attentive GAN for Predicting Paths Compliant to Social and Physical Constraints](https://mlsanity.com/paper/1806.01482/) (2018)
- [GenAD: Generative End-to-End Autonomous Driving](https://mlsanity.com/paper/2402.11502/) (2024)
- [Guided Motion Diffusion for Controllable Human Motion Synthesis](https://mlsanity.com/paper/2305.12577/) (2023)
- [MotionDiffuser: Controllable Multi-Agent Motion Prediction using Diffusion](https://mlsanity.com/paper/2306.03083/) (2023)
- [Diffusion-based Time Series Imputation and Forecasting with Structured State Space Models](https://mlsanity.com/paper/2208.09399/) (2022)
- [Stochastic Trajectory Prediction via Motion Indeterminacy Diffusion](https://mlsanity.com/paper/2203.13777/) (2022)
- [Scene Transformer: A unified architecture for predicting multiple agent trajectories](https://mlsanity.com/paper/2106.08417/) (2021)
- [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)
- [Latent Variable Sequential Set Transformers For Joint Multi-Agent Motion Prediction](https://mlsanity.com/paper/2104.00563/) (2021)
- [GroupNet: Multiscale Hypergraph Neural Networks for Trajectory Prediction with Relational Reasoning](https://mlsanity.com/paper/2204.08770/) (2022)
- [Implicit Latent Variable Model for Scene-Consistent Motion Forecasting](https://mlsanity.com/paper/2007.12036/) (2020)
- [Generative Skill Chaining: Long-Horizon Skill Planning with Diffusion Models](https://mlsanity.com/paper/2401.03360/) (2023)
- [TPNet: Trajectory Proposal Network for Motion Prediction](https://mlsanity.com/paper/2004.12255/) (2020)

## Built on by (most cited first, 5 of 5)

- [DeepSport: A Multimodal Large Language Model for Comprehensive Sports Video Reasoning via Agentic Reinforcement Learning](https://mlsanity.com/paper/2511.12908/) (2025)
- [GenTac: Generative Modeling and Forecasting of Soccer Tactics](https://mlsanity.com/paper/2604.11786/) (2026)
- [Modeling Matches as Language: A Generative Transformer Approach for Counterfactual Player Valuation in Football](https://mlsanity.com/paper/2603.15212/) (2026)
- [Social-Mamba: Socially-Aware Trajectory Forecasting with State-Space Models](https://mlsanity.com/paper/2605.15424/) (2026)
- [PathCRF: Ball-Free Soccer Event Detection via Possession Path Inference from Player Trajectories](https://mlsanity.com/paper/2602.12080/) (2026)

## Abstract (arXiv)

Generative models often treat continuous data and discrete events as separate processes, creating a gap in modeling complex systems where they interact synchronously. To bridge this gap, we introduce JointDiff, a novel diffusion framework designed to unify these two processes by simultaneously generating continuous spatio-temporal data and synchronous discrete events. We demonstrate its efficacy in the sports domain by simultaneously modeling multi-agent trajectories and key possession events. This joint modeling is validated with non-controllable generation and two novel controllable generation scenarios: weak-possessor-guidance, which offers flexible semantic control over game dynamics through a simple list of intended ball possessors, and text-guidance, which enables fine-grained, language-driven generation. To enable the conditioning with these guidance signals, we introduce CrossGuid, an effective conditioning operation for multi-agent domains. We also share a new unified sports benchmark enhanced with textual descriptions for soccer and football datasets. JointDiff achieves state-of-the-art performance, demonstrating that joint modeling is crucial for building realistic and controllable generative models for interactive systems. https://guillem-cf.github.io/JointDiff/