초록: Score-based Generative Models (SGMs) have significantly advanced high-dimensional data generation using stochastic differential equations (SDEs). Separately, Stochastic Partial Differential Equations (SPDEs) provide frameworks for modeling processes evolving in infinite-dimensional function spaces. While connections between SGMs and SPDEs are emerging, this work introduces a novel approach linking SPDEs to SGMs. We derive an error function from the Fokker-Planck equation associated with the reverse process of SGMs and hypothesize that we can model this error as an infinite-dimensional stochastic process. To apply this hypothesized connection, we propose a specific SPDE intended to govern this error process. We prove the existence and uniqueness of its solution, thereby ensuring our modeling approach is well-grounded. Building upon this validated SPDE formulation, we introduce the SPDE-Induced Evaluation Metric (SIEM). Developing a practical implementation for SIEM requires addressing the computational challenge posed by its inherent infinite-dimensionality; we achieve this through a spatial homogeneous Wiener process to reduce the problem to a one-dimensional calculation, and via denoising score matching, allowing us to utilize existing SGM implementations directly. Our experimental results demonstrate that SIEM works effectively across various datasets. These results show that our mathematical modeling is sound and also holds practical potential. Finally, we discuss the implications of our hypothesis and outline potential developments.