Modeling Score Approximation Errors in Diffusion Models via Forward SPDEs
Abstract
This study investigates the dynamics of Score-based Generative Models (SGMs) by treating the score estimation error as a stochastic source driving the Fokker-Planck equation. Departing from particle-centric SDE analyses, we employ an SPDE framework to model the evolution of the probability density field under stochastic drift perturbations. Under a simplified setting, we utilize this framework to interpret the robustness of generative models through the lens of geometric stability and displacement convexity. Furthermore, we introduce a candidate evaluation metric derived from the quadratic variation of the SPDE solution projected onto a radial test function. Preliminary observations suggest that this metric remains effective using only the initial 10% of the sampling trajectory, indicating a potential for computational efficiency.
Cite
@article{arxiv.2602.08579,
title = {Modeling Score Approximation Errors in Diffusion Models via Forward SPDEs},
author = {Junsu Seo},
journal= {arXiv preprint arXiv:2602.08579},
year = {2026}
}