将随机插值扩展到无限维希尔伯特空间，实现函数分布间高效生成桥接。
Stochastic Interpolants in Hilbert Spaces
- 提出无限维希尔伯特空间中随机插值的严格理论框架
- 在复杂偏微分方程基准上实现顶尖生成效果
- 适合需要跨函数分布生成的科学计算研究者
尽管扩散模型已成功应用于函数型数据，但能灵活连接任意分布的随机插值仍局限于有限维情形。本文通过建立无限维希尔伯特空间中随机插值的严谨理论框架，提供了适定性证明与显式误差界。该框架在条件生成任务中表现优异，尤其针对基于偏微分方程的复杂基准测试。所提方法实现了生成任意函数分布之间的桥梁，达到当前最优性能，为科学发现提供强大通用工具。
原文摘要 · Abstract (English)
Although diffusion models have successfully extended to function-valued data, stochastic interpolants -- which offer a flexible way to bridge arbitrary distributions -- remain limited to finite-dimensional settings. This work bridges this gap by establishing a rigorous framework for stochastic interpolants in infinite-dimensional Hilbert spaces. We provide comprehensive theoretical foundations, including proofs of well-posedness and explicit error bounds. We demonstrate the effectiveness of the proposed framework for conditional generation, focusing particularly on complex PDE-based benchmarks. By enabling generative bridges between arbitrary functional distributions, our approach achieves state-of-the-art results, offering a powerful, general-purpose tool for scientific discovery.
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