Read Sinho Chewi's textbook in canonical chapter order, with beginner exposition, rigorous contracts, and Lean evidence available on demand.
flowchart TD C1["1 · Langevin diffusion"] --> C2["2 · Functional inequalities"] C1 --> C3["3 · Stochastic analysis"] C2 --> C4["4 · Langevin Monte Carlo"] C3 --> C4 C4 --> C5["5 · Faster low-accuracy samplers"] C4 --> C6["6 · Rényi convergence"] C5 --> C6 C2 --> C7["7 · High-accuracy samplers"] C6 --> C7 C2 --> C8["8 · Proximal sampler"] C3 --> C9["9 · Lower bounds"] C6 --> C9 C8 --> C10["10 · Structured sampling"] C1 --> C11["11 · Non-log-concave sampling"] C3 --> C12["12 · Diffusion generative models"] C6 --> C12
Build the analytic language that turns Langevin dynamics into quantitative convergence estimates.
Develop Poincaré, log-Sobolev, transport, and isoperimetric tools, including semigroup proofs and preservation operations.
Build the stochastic-analysis tools used later for path-space comparison, conditioned diffusions, and bridge constructions.
Derive Langevin Monte Carlo guarantees through Wasserstein coupling, interpolation, convex optimization, and Girsanov comparison.
Study randomized midpoint, Hamiltonian, and underdamped methods that improve low-accuracy complexity.
Analyze LMC and ULMC in Rényi divergence using interpolation and Girsanov arguments.
Use accept/reject correction and conductance tools to obtain exact-target chains.
Study an augmented-variable sampler that isolates difficult geometry in a proximal subproblem.
Identify which dimension, smoothness, condition-number, and accuracy dependences are unavoidable.
Adapt Langevin analysis to stochastic gradients, coordinate updates, and mirror geometry.
Use Fisher information to formulate and analyze approximate stationarity for non-log-concave targets, then compare upper and lower bounds.
Connect sampling analysis to score-based reverse diffusions and generative modeling.