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:2607. 08757v1 Announce Type: cross Abstract: Score matching controls average error under the forward marginals, but a discretized reverse-time sampler evaluates the learned score along its own trajectory.
By Yiwei Zhou
arXiv:2506. 11378v3 Announce Type: replace Abstract: Sampling in score-based diffusion models can be performed by solving either a reverse-time stochastic differential equation (SDE) parameterized by an arbitrary stochasticity function or a probability flow ODE, corresponding to setting this stochasticity function to zero.
By Bernardo P. Schaeffer, Ricardo M. S. Rosa, Glauco Valle
The paper presents new Kullback–Leibler convergence guarantees for score diffusion models that avoid restrictive Lipschitz assumptions on the score function. By analyzing models with fixed step size derived from the Ornstein–Uhlenbeck semigroup and its kinetic counterpart, the authors derive simple, sharp KL bounds that hold for any data distribution with finite Fisher information relative to the standard Gaussian. This extends theoretical guarantees to a broader class of data distributions without requiring early stopping or compact support.
By Giovanni Conforti, Alain Durmus, Marta Gentiloni Silveri
arXiv:2610.27206v1 Announce Type: cross
Abstract: We study the sample complexity of estimating Ornstein--Uhlenbeck diffusion scores in $\mathbb R^d$ using denoising score matching (DSM) with finite-w...
By Fan Liu, Yahong Yang, Wei Zhu
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
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...
By Zhiyang Xun, Eric Price
The paper introduces Hessian-free high-resolution (HFHR) dynamics, an extension of underdamped Langevin dynamics that incorporates reversible position diffusion for sampling in machine learning. It provides an explicit quantitative contraction rate under a position Poincaré inequality, weighted Hessian and Laplacian bounds, and a compact Sobolev embedding, even when the potential is non‑convex. For the HFHR Monte Carlo algorithm, a path‑space Girsanov argument yields a non‑asymptotic convergence bound and an explicit iteration complexity in total variation distance, improving on previous HFHR results and demonstrating benefits of a positive diffusion parameter through numerical experiments.
By Wujun Lv, Xiaoyu Wang, Yingli Wang, Lingjiong Zhu
The paper establishes finite‑sample guarantees for fully discrete conditional diffusion models trained from data and run with a finite number of denoising steps. By aligning the score‑training objective with the sampling grid, the authors jointly analyze statistical estimation and numerical discretization errors. For any smoothness index β>0, they prove that an appropriately chosen grid yields an averaged conditional Kullback–Leibler divergence of ˗O_p(n^{-2β/(d_x+d_y+2β)}) and a total‑variation error of ˗O_p(n^{-β/(d_x+d_y+2β)}), matching known rates up to logarithmic factors.
By Qiuyun Zhu
arXiv:2511. 05940v3 Announce Type: replace-cross Abstract: Score-based diffusion models have emerged as a powerful class of generative methods, with successful applications across diverse domains.
By Kang Liu, Enrique Zuazua
arXiv:2501. 12982v3 Announce Type: replace-cross Abstract: This paper investigates how diffusion generative models leverage (unknown) low-dimensional structure to accelerate sampling.
By Jiadong Liang, Zhihan Huang, Yuxin Chen
arXiv:2610. 14567v2 Announce Type: replace-cross Abstract: This paper develops strong Gaussian approximations (KMT type) for constant learning rate stochastic gradient descent (SGD).
By Joseph Keslin, Wei Biao Wu