Topological Diffusion Transformers for Multi-Agent Trajectory Forecasting in Sparse Urban Spaces
Keywords:
topological data analysis, diffusion models, transformers, multi-agent trajectory forecasting, sparse urban spaces, infrastructure governance, fairness, sustainabilityAbstract
The accurate forecasting of multi-agent trajectories in urban environments is a critical capability for autonomous systems, traffic management, and urban planning. Traditional forecasting models often assume dense, homogeneous data distributions and rely on grid-based or fully connected architectures that become computationally prohibitive and statistically unreliable in sparse urban settings. This paper introduces a novel framework termed Topological Diffusion Transformers, which integrates topological data analysis, diffusion probabilistic models, and transformer attention mechanisms to enable robust trajectory prediction under conditions of data sparsity and irregular spatial connectivity. We examine the architectural foundations of this framework, emphasizing how topological priors derived from persistent homology can guide the attention process in transformers, while diffusion models provide a principled mechanism for generating multimodal trajectory distributions. The paper extends beyond technical design to address systemic considerations including computational infrastructure requirements, deployment scalability, governance of predictive uncertainty, fairness in heterogeneous agent populations, and sustainability of training regimes. We also discuss policy implications for smart city initiatives and autonomous vehicle networks, highlighting trade-offs between model expressivity, real-time inference constraints, and interpretability. Through cross-domain comparisons with established approaches in pedestrian forecasting, autonomous navigation, and social robotics, we illustrate the advantages and limitations of the proposed paradigm. The work aims to provide a comprehensive reference for researchers and practitioners seeking to deploy advanced forecasting systems in sparse, dynamic, and safety-critical urban environments.
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