📔 Foundations of Generative Models
Graduate Course, IISc, 2025
📌 Logistics: These notes have been compiled from lectures on the diffusion models by Prof. Sanjay Shakkottai; covering sampling theory, stochastic differential equations and functional inequalities, and modern diffusion- and flow-based generative models.
- Lec-1: Rejection, MH and Gibbs Sampling
- Lec-2: Langevin Sampling Setting
- Lec-3: SDE Basics and FP Equation
- Lec-4: Markov Processes
- Lec-4a: Characterization of Normal
- Lec-5: Poincare Inequality
- Lec-6: Bakry Emery Criterion
- Lec-7: Log Sobolev Inequality
- Lec-8: VAE and GANs (expanded notes)
- Lec-9: DDPM, DDIM and Tweedie’s Formula
- Lec-9a: MMSE and Fisher Information
- Lec-10: DDPM Training
- Lec-11: Ito Calculus
- Lec-12: LMC Wasserstein Coupling
- Lec-13: LMC Girsanov Thm
- Lec-14: DDPM Discretization
- Lec-15: Rectified Flow
- Lec-16: Posterior Sampling Overview
- Lec-17: PSLD-STSL
- Lec-18: RBMod-RFInv
- Lec-19: Conditional Flow Matching
- Lec-20: Hardness of Posterior Sampling
- Lec-21: Annealing and Smoothed Analysis
- Lec-22: Diffusion Language Models
- Lec-23: Discrete Flow Matching
- Lec-24: IGD