Modeling Score Approximation Errors in Diffusion Models via Forward SPDEs
Fuente:
arXiv
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| Autore principale: | |
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| Natura: | Preprint |
| Pubblicazione: |
2026
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| _version_ | 1866911434450927616 |
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| author | Seo, Junsu |
| author_facet | Seo, Junsu |
| 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. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2602_08579 |
| institution | arXiv |
| publishDate | 2026 |
| record_format | arxiv |
| spellingShingle | Modeling Score Approximation Errors in Diffusion Models via Forward SPDEs Seo, Junsu Machine Learning 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. |
| title | Modeling Score Approximation Errors in Diffusion Models via Forward SPDEs |
| topic | Machine Learning |
| url | https://arxiv.org/abs/2602.08579 |