A Mathematical Introduction to Diffusion Models

• URL: http://arxiv.org/abs/2607.01693v1
• Date: Thu, 02 Jul 2026 04:37:16 GMT
• Title: A Mathematical Introduction to Diffusion Models
• Abstract summary: These notes give a proof-oriented introduction to diffusion models from the viewpoint of sampling.<n>The intended audience is beginning graduate students with a background in probability but no prior exposure to differential equations, numerics, or diffusion models.
• Score: 6.765519834154584
• License: http://creativecommons.org/licenses/by/4.0/
• Abstract: These notes give a proof-oriented introduction to diffusion models from the viewpoint of sampling, tracing a single arc from classical sampling dynamics to modern diffusion samplers, their error analysis, and inference-time control. Throughout, the material is layered into core definitions and identities proved in full, representative estimates proved under simplifying assumptions, and research-level theorems stated with a proof roadmap. The intended audience is beginning graduate students with a background in probability but no prior exposure to stochastic differential equations, stochastic numerics, or diffusion models.

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