Modeling Score Approximation Errors in Diffusion Models via Forward SPDEs
This work addresses theoretical analysis for researchers in generative modeling, but it appears incremental as it builds on existing SPDE frameworks without major breakthroughs.
This study tackled the problem of understanding score estimation errors in diffusion models by modeling them as stochastic sources in a forward SPDE framework, resulting in a candidate evaluation metric that shows potential for computational efficiency by using only the initial 10% of the sampling trajectory.
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.