arXiv:2608.20635v1 Announce Type: cross Abstract: Discrete diffusion models have demonstrated strong performance across a range of datasets, including natural language data and graph-structured data....
arXiv:2610.02754v1 Announce Type: new Abstract: Diffusion models are highly developed in continuous spaces for image and video domains. Recently, major advances have been made for discrete diffusion...
arXiv:2502. 09151v3 Announce Type: replace Abstract: Diffusion models are one of the key architectures of generative AI.
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:2409. 18804v3 Announce Type: replace-cross Abstract: Denoising Diffusion Probabilistic Models (DDPM) are powerful state-of-the-art methods used to generate synthetic data from high-dimensional data distributions and are widely used for image, audio, and video generation as well as many more applications in science and beyond.
The paper presents a theoretical analysis of score mismatch in discrete diffusion models, deriving a KL divergence upper bound that quantifies the bias introduced when the training and target distributions differ. It examines partial-observation constraints such as text infilling and sentence completion, showing that the Conditional SEDD sampler can incur a bias that grows with dimension, vocabulary size, and compatibility. To mitigate this, the authors propose a Randomized Hard Clamping (RHC) sampler for coordinatewise set constraints, demonstrating through experiments that it effectively reduces bias and improves sampling performance.
arXiv:2607. 16685v1 Announce Type: cross Abstract: Conditional diffusion models have become a powerful and flexible framework for learning complex conditional distributions from labeled data.
The paper develops a statistical framework showing that empirical score matching can achieve minimax optimal performance for diffusion generative models when data lie on a low‑dimensional manifold. It establishes convergence rates for empirical risk minimization over constrained Sobolev classes and demonstrates that the resulting score estimators yield minimax optimal Wasserstein‑1 rates for the generated distribution, up to logarithmic factors. The analysis reveals that the statistical rates depend on the intrinsic dimension of the data manifold rather than its ambient dimension, providing conditions under which score‑based generative modeling generalizes rather than overfits.
arXiv:2606. 19894v1 Announce Type: new Abstract: The remarkable success of score-based diffusion models has spurred significant efforts to establish their theoretical foundations.
arXiv:2501. 12982v3 Announce Type: replace-cross Abstract: This paper investigates how diffusion generative models leverage (unknown) low-dimensional structure to accelerate sampling.
arXiv:2610.23404v1 Announce Type: new Abstract: Information-theoretic measures, such as Mutual Information (MI), play a crucial role in understanding non-linear relationships between random variables...
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.