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.

在微分方程生成建模领域中，我们首次引入了一种多维插值器，将这些系数扩展到多个维度上，在训练和推理阶段都使用单一维度标量值作为插值系数。此外，我们提出了一个新的路径优化问题，用于自适应确定多维推理轨迹，其中包括预定的微分方程求解器和固定数量的函数评估。我们的解决方案使用模拟动态和对抗性训练来优化推理路径。特别地，即使在没有路径优化的情况下，使用多维插值器在训练过程中也能提高模型的推理性能。当使用由我们的优化过程导出的自适应多维路径时，即使使用固定的求解器配置，也能进一步提高性能。多维插值器的引入不仅增强了模型的有效性，还开辟了在训练和推理方法论中探索的新领域，强调了多维路径作为一个未开发的前沿。