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| Main Author: | |
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| Format: | Preprint |
| Published: |
2026
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| Subjects: | |
| Online Access: | https://arxiv.org/abs/2602.08579 |
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Table of Contents:
- 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.