Trajectory prediction facilitates effective planning and decision-making, while constrained trajectory prediction integrates regulation into prediction. Recent advances in constrained trajectory prediction focus on structured constraints by constructing optimization objectives. However, handling unstructured constraints is challenging due to the lack of differentiable formal definitions. To address this, we propose a novel method for constrained trajectory prediction using a conditional generative paradigm, named Controllable Trajectory Diffusion (CTD). The key idea is that any trajectory corresponds to a degree of conformity to a constraint. By quantifying this degree and treating it as a condition, a model can implicitly learn to predict trajectories under unstructured constraints. CTD employs a pre-trained scoring model to predict the degree of conformity (i.e., a score), and uses this score as a condition for a conditional diffusion model to generate trajectories. Experimental results demonstrate that CTD achieves high accuracy on the ETH/UCY and SDD benchmarks. Qualitative analysis confirms that CTD ensures adherence to unstructured constraints and can predict trajectories that satisfy combinatorial constraints.

翻译：轨迹预测有助于实现有效的规划与决策，而约束轨迹预测则将规则整合到预测过程中。当前约束轨迹预测的研究进展主要集中于通过构建优化目标来处理结构化约束。然而，由于缺乏可微分的正式定义，处理非结构化约束具有挑战性。为此，我们提出了一种基于条件生成范式的新方法，用于约束轨迹预测，称为可控轨迹扩散（CTD）。其核心思想是：任何轨迹都对应着对约束的某种遵从程度。通过量化这种程度并将其视为条件，模型可以隐式地学习在非结构化约束下预测轨迹。CTD采用一个预训练的评分模型来预测遵从程度（即评分），并将该评分作为条件扩散模型的条件以生成轨迹。实验结果表明，CTD在ETH/UCY和SDD基准测试中实现了高精度。定性分析证实，CTD能够确保遵循非结构化约束，并能预测满足组合约束的轨迹。