Recent advances in infinite-dimensional diffusion models have demonstrated their effectiveness and scalability in function generation tasks where the underlying structure is inherently infinite-dimensional. To accelerate inference in such models, we derive, for the first time, an analog of the probability-flow ODE (PF-ODE) in infinite-dimensional function spaces. Leveraging this newly formulated PF-ODE, we reduce the number of function evaluations while maintaining sample quality in function generation tasks, including applications to PDEs.

翻译：近期无限维扩散模型的进展表明，在底层结构本质为无限维的函数生成任务中，此类模型具备高效性与可扩展性。为加速此类模型的推理过程，我们首次推导出无限维函数空间中概率流常微分方程（PF-ODE）的类比形式。通过运用这一新构建的PF-ODE，我们在保持函数生成任务（包括偏微分方程应用）样本质量的同时，显著减少了函数评估次数。