arXiv:2605. 17232v5 Announce Type: replace Abstract: Discrete diffusion has become a leading framework for generative modeling in various applications including language, vision, and biology.
By Kelvin Kan, Xingjian Li, Benjamin J. Zhang, Tuhin Sahai, Stanley Osher, Markos A. Katsoulakis
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.
By Vincent Pauline, Tobias H\"oppe, Kirill Neklyudov, Alexander Tong, Stefan Bauer, Andrea Dittadi
arXiv:2606. 16610v1 Announce Type: cross Abstract: Diffusion Flow Matching (DFM) has recently emerged as a versatile framework for generative modeling, yet its theoretical convergence properties remain only partially understood.
By Marta Gentiloni Silveri, Giovanni Conforti, Alain Durmus
arXiv:2605. 00161v2 Announce Type: replace Abstract: Diffusion language models (DLMs) are an attractive alternative to autoregressive models because they promise sublinear-time, parallel generation, yet practical gains remain elusive as high-quality samples still demand hundreds of refinement steps.
By Hasan Amin, Yuan Gao, Yaser Souri, Subhojit Som, Ming Yin, Rajiv Khanna, Xia Song
arXiv:2602. 15008v2 Announce Type: replace Abstract: Diffusion models over discrete spaces have recently shown striking empirical success, yet their theoretical foundations remain incomplete.
By Daniil Dmitriev, Zhihan Huang, Yuting Wei
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