Discrete denoising diffusion models (DDMs) have recently emerged as a compelling alternative to autoregressive (AR) modeling for discrete data, offering parallel generation and iterative global refinement capabilities. Unlike continuous diffusion, where the state space is fixed, DDMs are fundamentally shaped by how the discrete state space is constructed: the tokenization scheme, the vocabulary topology, and domain-specific structural alphabets.
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:2607. 01775v1 Announce Type: new Abstract: Discrete diffusion models have steadily improved in quality relative to autoregressive (AR) models.
By Marianne Arriola, Volodymyr Kuleshov
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:2607. 19686v1 Announce Type: cross Abstract: Masked diffusion models (MDMs) are a promising family of language generators, but achieving high-quality few-step generation remains challenging.
By Sijin Chen, Yinuo Ren, Heyang Zhao, Ziheng Cheng, Quanquan Gu, Lexing Ying
arXiv:2510. 22510v3 Announce Type: replace Abstract: While continuous diffusion has shown remarkable success in continuous domains such as image generation, its direct application to discrete data has underperformed pure discrete formulations.
By Patrick Pynadath, Jiaxin Shi, Ruqi Zhang
arXiv:2606. 18022v1 Announce Type: new Abstract: Masked diffusion models (MDMs) have recently emerged as a promising paradigm for sequence generation.
By Alba Carballo-Castro, Julianna Piskorz, Paulius Rauba, Mihaela van der Schaar, Pascal Frossard
PlaidQ is a 0.7B continuous diffusion language model designed for code generation. By distilling its iterative refinement trajectory into only a few denoising steps—or even a single step—PlaidQ achieves competitive performance with discrete diffusion models while dramatically reducing inference time. The study demonstrates that continuous diffusion can be effectively compressed, enabling efficient and accurate code generation with minimal computational overhead.
By Fred Zhangzhi Peng, Kaiwen Zheng, Anru R. Zhang
arXiv:2604. 26985v2 Announce Type: replace-cross Abstract: Masked diffusion models (MDMs) generate discrete sequences by iterative denoising under an absorbing masking process.
By Michael Cardei, Huu Binh Ta, Ferdinando Fioretto
arXiv:2610.02193v1 Announce Type: cross
Abstract: Discrete diffusion language models offer a compelling alternative to autoregressive generation for tasks demanding bidirectional reasoning and global...
By Hui Ren, Zihan Li, Chang Liu, Huidong Liu, Alexander Schwing
arXiv:2607. 14106v1 Announce Type: cross Abstract: In this paper we introduce token time continuous diffusion (TTCD), a new diffusion language model which (a) operates in continuous space, deterministically mapping Gaussian noise to a final token canvas with no further sampling, and crucially (b) incorporates a new notion of per-token times, with some tokens proceeding from noise to token at a faster rate than others.
By Parikshit Bansal, Sujay Sanghavi
arXiv:2603. 02230v2 Announce Type: replace-cross Abstract: Self-correction is an effective technique for maintaining parallel sampling in discrete diffusion models with minimal performance degradation.
By Linxuan Wang, Ziyi Wang, Yikun Bai, Wei Deng, Guang Lin, Qifan Song