arXiv Machine Learning
Jul 2
Accelerating Discrete Diffusion Models with Parallel-In-Time Sampling
arXiv:2607. 00773v1 Announce Type: new Abstract: Discrete diffusion models are widely used for learning and generating discrete distributions.
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.
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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
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 Machine Learning
Jul 2
Fast Score-Based Sampling via Log-Concave Reductions
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 AI
4d ago
Query Lower Bounds for Diffusion Sampling
arXiv:2604.10857v2 Announce Type: replace-cross Abstract: Diffusion models generate samples by iteratively querying learned score estimates. A rapidly growing literature focuses on accelerating sampl...
arXiv Machine Learning
Sep 10
Vocabulary-size-independent Convergence of Discrete Diffusion Models: adjoint equations induce the right space
arXiv:2605. 17232v5 Announce Type: replace Abstract: Discrete diffusion has become a leading framework for generative modeling in various applications including language, vision, and biology.
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
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.
arXiv Statistics ML
2d ago
Sample complexity bounds for categorical Markov random fields via Discrete Diffusions
arXiv:2610.02128v1 Announce Type: cross Abstract: Many applications in statistics, economics, and physics require sampling from high-dimensional categorical distributions with local dependence struct...
arXiv Machine Learning
4d ago
Sharp Convergence and Sampling Trade-offs for Riemannian Diffusion under Nonnegative Ricci Curvature
arXiv:2609.36568v1 Announce Type: new Abstract: Diffusion models have emerged as state-of-the-art generative models, with recent extensions from Euclidean spaces to Riemannian manifolds. However, exi...
arXiv Machine Learning
Aug 24
Minimax Optimality of Score-Entropy Discrete Diffusion
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 Statistics ML
Aug 26
A Non-asymptotic Analysis for Learning and Applying a Preconditioner in MCMC
The paper presents a non‑asymptotic analysis of Markov chain Monte Carlo (MCMC) algorithms that learn and apply a preconditioner based on either the target covariance or the expected Hessian of the target potential. It compares the finite‑time computational costs of these preconditioned schemes with unpreconditioned counterparts, providing guarantees for algorithms such as the Unadjusted Langevin Algorithm (ULA) and the proximal sampler. The analysis relies on a contraction assumption in the Wasserstein‑2 distance to formalize approximate independence and bridge modern MCMC theory with classical effective sample size heuristics.