In the domain of differential equation-based generative modeling, conventional approaches often rely on single-dimensional scalar values as interpolation coefficients during both training and inference phases. In this work, we introduce, for the first time, a multidimensional interpolant that extends these coefficients into multiple dimensions, leveraging the stochastic interpolant framework. Additionally, we propose a novel path optimization problem tailored to adaptively determine multidimensional inference trajectories, with a predetermined differential equation solver and a fixed number of function evaluations. Our solution involves simulation dynamics coupled with adversarial training to optimize the inference path. Notably, employing a multidimensional interpolant during training improves the model's inference performance, even in the absence of path optimization. When the adaptive, multidimensional path derived from our optimization process is employed, it yields further performance gains, even with fixed solver configurations. The introduction of multidimensional interpolants not only enhances the efficacy of models but also opens up a new domain for exploration in training and inference methodologies, emphasizing the potential of multidimensional paths as an untapped frontier.

翻译：在基于微分方程的生成建模领域，传统方法通常将单维标量值作为训练和推理阶段的插值系数。本文首次提出一种基于随机插值框架的多维插值函数，将插值系数扩展至多维度。同时，我们针对预定义微分方程求解器与固定函数评估次数，设计了一种自适应确定多维推理轨迹的新型路径优化问题。所提解决方案通过仿真动力学与对抗训练相结合的方式优化推理路径。值得注意的是，即使未进行路径优化，训练阶段采用多维插值函数仍能提升模型推理性能。当采用经优化过程得到的自适应多维路径时，即便使用固定求解器配置，模型性能也能获得进一步增益。多维插值函数的引入不仅增强了模型效能，更为训练和推理方法学开辟了新的探索领域，凸显了多维路径作为未开发前沿的巨大潜力。