Modeling Score Approximation Errors in Diffusion Models via Forward SPDEs

TL;DR

This paper models score approximation errors in diffusion models using forward SPDEs, providing insights into robustness and proposing an efficient evaluation metric based on early sampling dynamics.

Contribution

It introduces an SPDE-based framework for analyzing score errors in diffusion models and proposes a new metric for early-stage evaluation of generative quality.

Findings

The proposed metric remains effective with only 10% of the sampling trajectory.

SPDE framework offers a new perspective on robustness via geometric stability.

Preliminary results indicate potential for computational efficiency in evaluation.

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.