arXiv:2608. 13520v1 Announce Type: cross Abstract: We study masking diffusion for discrete sampling and introduce a path-resolved measure of data geometry called the \emph{unmasking growth complexity} ({\textsf{UGC}\xspace}).
By Martin J. Wainwright
arXiv:2608.28949v1 Announce Type: cross
Abstract: We study a class of product-reference diffusion algorithms for sampling from a discrete distribution. We show that their sampling performance can be...
By Martin J. Wainwright
arXiv:2602. 15008v2 Announce Type: replace Abstract: Diffusion models over discrete spaces have recently shown striking empirical success, yet their theoretical foundations remain incomplete.
By Daniil Dmitriev, Zhihan Huang, Yuting Wei
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.
By Daniil Dmitriev, Zhihan Huang, Yuting Wei
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.
By M. J. Wainwright
The paper studies how to choose sampling schedules for tau‑leaping in masked discrete diffusion models. By deriving an exact integral representation of the factorization error ε_fact in terms of a dependence density ρ, the authors develop estimators and recursive equations that identify the unique optimal schedule under a monotonicity condition. In the large‑scale limit, they provide explicit characterizations of the optimal smooth schedule and show that while optimizing smooth schedules can improve constants, it does not change the N/K scaling unless the dependence density degenerates, in which case asymptotic improvements are possible.
By Cecilia Secchi, Giacomo Zanella