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.
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. 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.
arXiv:2509. 23937v5 Announce Type: replace-cross Abstract: Diffusion models transform noise into data by injecting information that was captured in their neural network during the training phase.
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:2605. 10938v2 Announce Type: replace-cross Abstract: Diffusion and flow-based models have become the de facto approaches for generating continuous data, e.
arXiv:2605. 07971v2 Announce Type: replace-cross Abstract: We introduce Discrete Voxel Diffusion (DVD), a discrete diffusion framework to generate, assess, and edit sparse voxels for SLat (Structured LATent) based 3D generative pipelines.
arXiv:2606. 00094v1 Announce Type: cross Abstract: Image generative models aim to sample data points from the underlying data manifold, a task that requires learning and decoding a dense, low-dimensional, and compact parameterization space.
arXiv:2608.10615v2 Announce Type: replace Abstract: Discrete diffusion models for categorical generation are defined by a corruption kernel, which determines the intermediate state space and the asso...
arXiv:2602. 19066v2 Announce Type: replace-cross Abstract: Diffusion Language Models (DLMs) have recently achieved strong results in text generation.
arXiv:2607. 10580v1 Announce Type: cross Abstract: AI models are increasingly trained on personal images scraped from social media and public platforms, often without consent, leading to serious privacy violations, such as unauthorized facial recognition and targeted advertising.
arXiv:2606. 01024v1 Announce Type: cross Abstract: Discrete Masked diffusion language models generate text by iterative parallel decoding, but few-step decoding suffers from a tradeoff between length and quality: with a fixed step budget, standard methods can generate a short, high-quality output, or they can produce long but repetitive text.
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.