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.
Primary theorem authority stays explicit. Chewi's book controls the source-facing theorem; Chewi's official supplement is additional source material. Other textbooks are used to recover standard omitted prerequisites or rigorous details and never silently alter the pinned theorem.
Primary theorem order and source-facing statement authority.
Open textbook ↗Official material omitted from the book for space. Samplinglib treats it as source material attached to Chapter 2, not as an ASTIS derivation.
Open supp.pdf ↗Used when Chewi sketches standard stochastic-calculus details and formalization requires the hidden measurability, stopping, completion, or martingale hypotheses to be made explicit.
Chewi's bibliographical notes point readers to standard books when the main text omits routine or technical proofs. Samplinglib uses these as background/rigor references, never as silent replacements for the pinned Chewi theorem.
Used to expand concentration, isoperimetry, and functional-inequality arguments around Chapter 2 when the source presentation is intentionally compact.