🤖 AI Summary
This work addresses the unclear impact of score estimation errors on generation quality and stability in existing diffusion models. It introduces, for the first time, a stochastic partial differential equation (SPDE) framework that models score errors as stochastic sources, characterizing the evolution of the probability density field via a forward SPDE. This field-theoretic perspective enables rigorous analysis of geometric stability and displacement convexity in the generative process. The study further proposes a novel quadratic variational metric based on projections onto radial test functions, which efficiently evaluates model performance using only the first 10% of sampling trajectories. This approach not only substantially improves evaluation efficiency but also deepens the understanding of score error dynamics.
📝 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.