{"ID":5675124,"CreatedAt":"2026-07-03T01:40:09.565152011Z","UpdatedAt":"2026-07-05T04:25:12.31577563Z","DeletedAt":null,"paper_url":"https://arxiv.org/abs/2607.01693","arxiv_id":"2607.01693","title":"A Mathematical Introduction to Diffusion Models","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.","short_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...","url_abs":"https://arxiv.org/abs/2607.01693","url_pdf":"https://arxiv.org/pdf/2607.01693v1","authors":"[\"Jianfeng Lu\"]","published":"2026-07-02T04:37:16Z","proceeding":"cs.LG","tasks":"[\"cs.LG\",\"math.PR\"]","methods":"[\"Diffusion Model\"]","has_code":false}