arXiv:2607. 00773v1 Announce Type: new Abstract: Discrete diffusion models are widely used for learning and generating discrete distributions.
arXiv:2602. 15008v2 Announce Type: replace Abstract: Diffusion models over discrete spaces have recently shown striking empirical success, yet their theoretical foundations remain incomplete.
arXiv:2606. 24140v1 Announce Type: new Abstract: Discrete flow matching (DFM) provides a principled framework for generative modeling on discrete state spaces via continuous-time Markov chain dynamics.
arXiv:2507. 08390v5 Announce Type: replace Abstract: Discrete diffusion models have recently emerged as strong alternatives to autoregressive language models, matching their performance through large-scale training.
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.
arXiv:2607. 26285v1 Announce Type: cross Abstract: Two central challenges in diffusion-based sampling are the theoretical one of understanding their remarkable effectiveness even in high-dimensional settings, and the practical one of designing algorithms with certified performance guarantees.
GeoSPRINT is a training‑free framework that constructs non‑uniform sampling schedules for diffusion model inference by detecting geometrically redundant steps in denoising trajectories. It uses a hyperplanarity test in latent space, implemented via QR factorization, to allocate more steps to high‑curvature regions, and introduces the trajectory projection score α_traj as a model‑free diagnostic for flow quality. Across CIFAR‑10, LSUN Church, and Stable Diffusion v1.5, GeoSPRINT consistently outperforms uniform DDIM schedules at matched NFE budgets, improving FID scores by up to 1.93 points.
The paper proves that for discrete diffusion models using uniform or remasking forward processes, an adaptive sampler based on a leave‑one‑out denoiser can achieve sampling error proportional to the score‑estimation error plus a small tolerance. The required number of discretization steps scales with the dual total correlation of the target distribution, not directly with the ambient dimension. This result shows that sampling complexity is governed by the intrinsic dependence structure of the distribution, and the authors provide an information‑theoretic analysis linking discretization error to mutual information between coordinates.
Discrete flow matching (DFM) provides a principled framework for generative modeling on discrete state spaces via continuous-time Markov chain dynamics. In practice, sampling for DFM commonly employs discretizations such as $τ$-leaping, yet efficient sampling methods under a limited number of function evaluations (NFE) remain less studied.
arXiv:2603.00763v2 Announce Type: replace Abstract: Text-to-image diffusion models have achieved unprecedented success but still struggle to produce high-quality results under limited sampling budget...
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.
The paper introduces PiX-MC, a time‑parallel posterior sampling framework that combines proximal Langevin dynamics with Picard iteration for Bayesian imaging inverse problems. By leveraging efficient proximal operators for many imaging likelihoods and exploiting parallelism across discretization nodes, PiX-MC supports multi‑GPU implementation and includes multi‑block and annealed variants to enhance scalability. Experiments on various imaging tasks, including a large‑scale sparse‑view CT problem, show that PiX‑MC can reduce runtime by up to 50× while maintaining reconstruction quality.
arXiv:2506. 13058v2 Announce Type: replace-cross Abstract: Diffusion probabilistic models (DPMs) have demonstrated remarkable success in visual generation.