Modeling Score Approximation Errors in Diffusion Models via Forward SPDEs
On the map: Diffusion models → Diffusion foundations and sampling
Abstract (arXiv)
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.
Key facts. No citing papers in the map yet (data through 7 Oct 2026). Placed in Diffusion foundations and sampling, one of 14 directions in Diffusion models. Builds on 12 of its 28 references that are in the map. First posted on arXiv 9 Feb 2026.
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12 of 28 references.
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- 2024Score-based generative models are provably robust: an uncertainty quantification perspective24 May
- 2024Convergence Analysis of Probability Flow ODE for Score-based Generative Models15 Apr
- 2022Sampling is as easy as learning the score: theory for diffusion models with minimal data assumptions22 Sep
- 2020Score-Based Generative Modeling through Stochastic Differential Equations26 Nov
- 2020Denoising Diffusion Probabilistic Models19 Jun
Other references · 7
- 2015U-Net: Convolutional Networks for Biomedical Image Segmentationcited by 19,604
- 2019Generative Modeling by Estimating Gradients of the Data Distributioncited by 4,067
- 2022Diffusion Posterior Sampling for General Noisy Inverse Problemscited by 1,375
- 2015LSUN: Construction of a Large-scale Image Dataset using Deep Learning with Humans in the Loopcited by 1,350
- 2022Denoising Diffusion Restoration Modelscited by 951
- 2022Statistical Efficiency of Score Matching: The View from Isoperimetrycited by 63
- 2024Wavelet Diffusion Neural Operatorcited by 28
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Close in wording, no citation either way
- 2025A PDE Perspective on Generative Diffusion Models
- 2023Closing the ODE-SDE gap in score-based diffusion models through the Fokker-Planck equation
- 2026On the Robustness of Langevin Dynamics to Score Function Error
- 2022FP-Diffusion: Improving Score-based Diffusion Models by Enforcing the Underlying Score Fokker-Planck Equation
- 2021Score-Based Generative Modeling with Critically-Damped Langevin Diffusion
- 2024Discrete vs. Continuous Trade-offs for Generative Models
- 2025A Malliavin calculus approach to score functions in diffusion generative models
- 2023Improved Convergence of Score-Based Diffusion Models via Prediction-Correction