A PDE Perspective on Generative Diffusion Models

arXiv:2511.05940 · math.OC, cs.AI, math.AP · Submitted 2025-11-08 · Read on arXiv

math.OC, cs.AI, math.AP

Submitted: 2025-11-08

Updated: 2026-10-07

Comments: 39 pages, 4 figures

License: http://arxiv.org/licenses/nonexclusive-distrib/1.0/

Terminology

• Diffusion Model — 4× in this paper · explained in 9 episodes
• Diffusion Models — 4× in this paper · explained in 6 episodes
• Fidelity — 2× in this paper · explained in 2 episodes
• Consistency — 1× in this paper · explained in 3 episodes
• Diffusion Processes — 1× in this paper · explained in 2 episodes

Sources

• Memorization and Regularization in Generative Diffusion Models
• On Memorization in Diffusion Models
• A Good Score Does not Lead to A Good Generative Model
• Resolving Memorization in Empirical Diffusion Model for Manifold Data in High-Dimensional Spaces
• On the Generalization of Diffusion Model
• Asymptotic behavior of scalar convection-diffusion equations

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