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.
arXiv:2607. 13431v1 Announce Type: cross Abstract: 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.
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: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.
arXiv:2607. 01775v1 Announce Type: new Abstract: Discrete diffusion models have steadily improved in quality relative to autoregressive (AR) models.
arXiv:2606. 09962v1 Announce Type: cross Abstract: Continuous diffusion for categorical data is a framework belonging to the diffusion family and aiming at generating discrete data.
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.
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.
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...
arXiv:2606. 18022v1 Announce Type: new Abstract: Masked diffusion models (MDMs) have recently emerged as a promising paradigm for sequence generation.
The paper introduces Clock Diffusion, a framework for semi‑autoregressive continuous diffusion language models that incorporates position‑dependent noise schedules, efficient training, and sampling algorithms. It presents two generation modes—block and sliding window—and defines ClockDLMs, a family of Gaussian models that achieve state‑of‑the‑art diffusion likelihoods on OpenWebText and outperform continuous baselines on GSM8K while matching or exceeding discrete diffusion models. The authors also propose Cache Grab, a set of efficient samplers that adapt accelerated inference techniques from discrete diffusion to further improve model quality and efficiency.
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.
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.