A Mathematical Introduction to Diffusion Models
- Published
- Source
- arXiv
- Paper number
- 550
- Field
- Machine Learning
- arXiv ID
- 2607.01693
Key points
- The convergence guarantees of Langevin dynamics and ULA and MALA are proved through KL contraction under log-Sobolev inequalities.
- The Tweedie identity and the reverse-time SDE form the theoretical backbone of diffusion models, while the same Gaussian channel is reinterpreted through Polchinski flow and probabilistic localization.
- The discretization error of DDPM is decomposed into three terms, early stopping, KL telescoping, and score error, for analysis.
- Discrete diffusion models replace the noising SDE with a continuous-time Markov chain and reframe the error analysis in finite state spaces.
- It systematizes guidance, reward tilting, path-space control, and inference-time reinforcement learning as ways to steer trained models at inference time.
- More than 50 references and appendices on Itô calculus and Gaussian tools make the work self-contained.
Paper links
External research summaries. These are not HDATF publications or measured product results.