🎓 I’m teaching CIS 6270: Discrete Generative Models at @Penn this fall! It’s a math-first course on modern generative modeling across continuous and discrete spaces, with full derivations, code, worked examples, and current research. Follow along with us this semester! 👇 cis6270.github.io/ We start this semester with core probability, ODEs/SDEs, the continuity and Fokker-Planck equations, and then derive flow matching and score matching through DDPM, DDIM, probability-flow ODEs, along with both single- and multi-objective guidance. 🌊 Then, we rebuild the story in discrete space. 🎲 That means CTMCs and master equations, time reversal, MDLM, D3PM, block diffusion, discrete scores and guidance, followed by discrete flow matching with jump processes and simplex-based flows. 🦘 We also go well beyond the standard material: multi-objective guidance, rectified flows, and a full lecture on modern flow maps, including consistency + shortcut models, categorical/discrete flow maps, Meta Flow Maps, expanding state spaces, and strong stochastic flow maps. 🗺️ We finish by connecting generation to optimal transport, stochastic optimal control, and path-space methods, working from Wasserstein geometry and Sinkhorn through Girsanov, Doob transforms, Schrödinger bridges, and modern continuous and discrete bridge-matching methods. 🌉 Throughout the semester, on the website, we’ll be releasing the lecture slides (you can see how deliberate they are!), project descriptions, exams + full solutions, and accompanying code on HuggingFace! 🤗 Our goal is that someone can start from the foundations and follow the math all the way to the newest papers. 📚 By the end, you should have the tools to turn your own research ideas into papers for the main conferences. Just promise me we won’t be the reason ICLR goes from 60k submissions to 70k! 😅 I’m incredibly grateful to my TAs (also my PhD students), for helping me build and teach all of this: @SophieVincoff @TongChen321 @RosieZ0512! 🥰 We hope you enjoy the material! 🥳