Simulation-Free Flow/Transport/Diffusion Generative Models from First Principles — with Historical Context
A first-principles introduction to transport, diffusion, and flow-based generative models—covering foundational ideas and historical context.
In addition to the usual references on diffusion models and normalizing flows, the following papers are especially noteworthy and influential:
- Anderson (1982). Reverse-time diffusion equation models
- Boffi, Vanden-Eijnden (2022). Probability flow solution of the Fokker-Planck equation
- Hyvärinen (2005). Estimation of non-normalized statistical models by score matching
- Sohl-Dickstein, Weiss, Maheswaranathan, Ganguli (2015). Deep unsupervised learning using nonequilibrium thermodynamics
- Maoutsa, Reich, Opper (2020). Interacting particle solutions of Fokker-Planck equations through gradient-log-density estimation
- Jarzynski (1997). Targeted free energy perturbation
- Vargas, Padhy, Blessing, Nüsken (2024). Transport meets Variational Inference: Controlled Monte Carlo Diffusions
- Milanfar (2020). From Regression to Attention: A six decade journey