PlayGen-MoG: Framework for Diverse Multi-Agent Play Generation via Mixture-of-Gaussians Trajectory Prediction

Modeling open-play soccer tactics is a formidable challenge due to the stochastic, multi-agent nature of the game. Existing computational approaches typically produce single, deterministic trajectory forecasts or focus on highly structured set-pieces, fundamentally failing to capture the inherent variance and branching possibilities of real-world match evolution. Here, we introduce GenTac, a diffusion-based generative framework that conceptualizes soccer tactics as a stochastic process over continuous multi-player trajectories and discrete semantic events. By learning the underlying distribution of player movements from historical tracking data, GenTac samples diverse, plausible, long-horizon future trajectories. The framework supports rich contextual conditioning, including opponent behavior, specific team or league playing styles, and strategic objectives, while grounding continuous spatial dynamics into a 15-class tactical event space. Extensive evaluations on our proposed benchmark, TacBench, demonstrate four key capabilities: (1) GenTac achieves high geometric accuracy while strictly preserving the collective structural consistency of the team; (2) it accurately simulates stylistic nuances, distinguishing between specific teams (e.g., Auckland FC) and leagues (e.g., A-League versus German leagues); (3) it enables controllable counterfactual simulations, demonstrably altering spatial control and expected threat metrics based on offensive or defensive guidance; and (4) it reliably anticipates future tactical outcomes directly from generated rollouts. Finally, we demonstrate that GenTac can be successfully trained to generalize to other dynamic team sports, including basketball, American football, and ice hockey.

Success in association football relies on both individual skill and coordinated tactics. While recent advancements in spatio-temporal data and deep learning have enabled predictive analyses like trajectory forecasting, the development of tactical design remains limited. Bridging this gap is essential, as prediction reveals what is likely to occur, whereas tactic generation determines what should occur to achieve strategic objectives. In this work, we present TacticGen, a generative model for adaptable and scalable tactic generation. TacticGen formulates tactics as sequences of multi-agent movements and interactions conditioned on the game context. It employs a multi-agent diffusion transformer with agent-wise self-attention and context-aware cross-attention to capture cooperative and competitive dynamics among players and the ball. Trained with over 3.3 million events and 100 million tracking frames from top-tier leagues, TacticGen achieves state-of-the-art precision in predicting player trajectories. Building on it, TacticGen enables adaptable tactic generation tailored to diverse inference-time objectives through classifier guidance mechanism, specified via rules, natural language, or neural models. Its modeling performance is also inherently scalable. A case study with football experts confirms that TacticGen generates realistic, strategically valuable tactics, demonstrating its practical utility for tactical planning in professional football. The project page is available at: https://shengxu.net/TacticGen/.

Deepgenerative models havebecomeapromisingapproach for human motion prediction due to their ability to capture multimodal distributions and represent diverse human be haviors. However, generating predictions that are both di verse and jointly consistent among interacting agents re mains challenging. In addition, most existing approaches are primarily evaluated using single-agent (marginal) met rics, which fail to fully reflect the joint dynamics of multi agent interactions. We propose a diffusion-based frame work that improves multi-agent motion prediction by lever aging rich contextual information from historical trajecto ries. This information is incorporated through a guidance mechanism to enhance the diversity and expressiveness of predicted motions. To further enforce interaction consis tency, we introduce an energy-based formulation that re fines the joint trajectory distribution while preserving the plausibility of individual trajectories. Extensive experi ments on four benchmark datasets demonstrate that our approach consistently outperforms existing methods. No tably, our approach substantially improves both marginal (ADE/FDE) and joint (JADE/JFDE) metrics on ETH/UCY over strong marginal baselines. Compared with prior joint prediction methods, it delivers significant gains in marginal metrics while maintaining competitive joint performance.