arXiv AI
The information geometry of product-reference discrete diffusion: Interaction growth complexity and optimal scheduling
Read the original on arXiv AI →The Flow has not summarised this story yet — read it at arXiv AI.
Related stories
arXiv Machine Learning
Jul 30
Denoising growth complexity: Data geometry and certified schedules for diffusion sampling
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 AI
Aug 14
The data geometry of masking diffusion: Certified-optimal schedules via unmasking growth complexity
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}).
arXiv Machine Learning
Jul 1
Efficient Sampling with Discrete Diffusion Models: Sharp and Adaptive Guarantees
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 Machine Learning
Sep 23
Statistical Rates for Entropic Optimal Transport in the Discrete to SubGaussian Regime
arXiv:2609. 26647v1 Announce Type: cross Abstract: We study statistical rates in entropic optimal transport in the semi-discrete regime where one measure has finite support and the other is subGaussian.
arXiv Statistics ML
Aug 25
Provably adaptive sampling with uniform and remasking discrete diffusion models
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 Machine Learning
Sep 21
Schedule optimization for tau-leaping in masked discrete diffusion
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.