arXiv:2512. 24152v2 Announce Type: replace-cross Abstract: Sampling based on score diffusions has led to striking empirical results, and has attracted considerable attention from various research communities.
arXiv:2602. 15008v2 Announce Type: replace Abstract: Diffusion models over discrete spaces have recently shown striking empirical success, yet their theoretical foundations remain incomplete.
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.
arXiv:2506. 13061v4 Announce Type: replace Abstract: Diffusion probabilistic models generate samples by learning to reverse a noise-injection process that transforms data into noise.
arXiv:2501. 12982v3 Announce Type: replace-cross Abstract: This paper investigates how diffusion generative models leverage (unknown) low-dimensional structure to accelerate sampling.
arXiv:2602. 08026v2 Announce Type: replace Abstract: We analyse linear ensemble sampling (ES) with standard Gaussian perturbations in stochastic linear bandits.
The paper studies how to allocate a fixed computational budget across the denoising steps of diffusion models to improve sample quality at deployment. It shows that the expected benefit of evaluating multiple candidates at a step can be decomposed into a step‑specific sensitivity and a universal sample‑size factor, and that the optimal allocation follows a water‑filling structure. Experiments demonstrate that this allocation achieves the same quality as a uniform strategy while reducing function evaluations by 20–50%.
arXiv:2607. 14398v1 Announce Type: cross Abstract: Constrained generative models aim to produce samples that satisfy complex feasibility constraints while remaining faithful to the data distribution.
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:2606. 11149v1 Announce Type: new Abstract: We study the problem of learning a drifting concept in the presence of Massart noise.
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.
arXiv:2608. 18237v1 Announce Type: cross Abstract: Estimating the difference of two Stein's score functions is a fundamental problem in generative modeling.