arXiv:2607. 01693v1 Announce Type: new Abstract: These notes give a proof-oriented introduction to diffusion models from the viewpoint of sampling, tracing a single arc from classical sampling dynamics to modern diffusion samplers, their error analysis, and inference-time control.
Parameter estimation in stochastic differential equations is a classical statistical problem of much importance in many scientific fields. Recent work of Tapia Costa et al.
arXiv:2606. 02115v1 Announce Type: cross Abstract: Parameter estimation in stochastic differential equations is a classical statistical problem of much importance in many scientific fields.
arXiv:2606. 01645v1 Announce Type: cross Abstract: Diffusion models have emerged as a leading framework for deep generative modeling.
The article "Foundations of Diffusion Models in General State Spaces: A Self-Contained Introduction" presents a unified primer on diffusion models that applies to both continuous Euclidean data and discrete categorical structures. It develops discrete-time forward noising via Markov kernels and learned reverse dynamics, and connects these to continuous-time limits such as stochastic differential equations in ρ^d and continuous-time Markov chains on finite alphabets, deriving the corresponding Fokker–Planck and master equations. The work also shows how different forward corruption choices—Gaussian processes for continuous spaces and structured categorical transition kernels for discrete spaces—affect reverse dynamics and the evidence lower bound used in training, offering a layered exposition for newcomers, practitioners, and experts alike.
arXiv:2606. 15835v1 Announce Type: cross Abstract: Diffusion models have achieved impressive empirical success in generative tasks, and their convergence theory is now relatively well understood.
arXiv:2607.04780v2 Announce Type: replace-cross Abstract: Post-hoc conditioning of pretrained diffusion models can be addressed using Sequential Monte Carlo (SMC) methods. By evolving an interacting...
The paper establishes a first‑order theoretical framework for diffusion models, showing that SDE‑based reverse‑time flows of both overdamped and underdamped Langevin diffusions contract relative Fisher divergences at explicit exponential rates when the stationary potential of the forward process is strongly convex. It further incorporates discretization to provide averaged first‑order stationarity bounds—sampling analogues of averaged gradient‑norm guarantees in nonconvex optimization—for samplers of both diffusion models. These results highlight a unique advantage of SDE‑based reverse diffusion over ODE‑based approaches, offering local convexity‑free certificates that ensure score consistency rather than global mode weights.
arXiv:2505. 06800v2 Announce Type: replace-cross Abstract: Diffusion-based generative models have renewed interest in stochastic differential equation methods for sampling from complex distributions.
Sequential Monte Carlo (SMC) methods are a natural tool for post-hoc conditioning of pretrained generative models, but in many applications the mutation kernels used by the particle system are biased approximations of an ideal Feynman--Kac flow. This paper develops a non-asymptotic error analysis for such SMC samplers.
arXiv:2609. 17577v1 Announce Type: cross Abstract: We study Langevin diffusion and Langevin Monte Carlo (LMC) when the target distribution changes over time.