arXiv:2608. 02799v1 Announce Type: cross Abstract: Score-based diffusion models are typically formulated using continuous-time stochastic differential equations and measure-theoretic stochastic calculus.
By Sunder Ram Krishnan
arXiv:2609.00279v1 Announce Type: cross
Abstract: This work shows that diffusion models learned with standard denoising loss can provide effective global MCMC proposals for complex high-dimensional t...
By Mitch Hill
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.
By Jairon H. N. Batista, Fl\'avio B. Gon\c{c}alves, Yuri F. Saporito, Rodrigo S. Targino
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.
By Zhifeng Chen, Chenyang Jiang, Yazhen Wang
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:2501. 12982v3 Announce Type: replace-cross Abstract: This paper investigates how diffusion generative models leverage (unknown) low-dimensional structure to accelerate sampling.
By Jiadong Liang, Zhihan Huang, Yuxin Chen