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: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:2506. 13061v4 Announce Type: replace Abstract: Diffusion probabilistic models generate samples by learning to reverse a noise-injection process that transforms data into noise.
By Daniel Zhengyu Huang, Jiaoyang Huang, Zhengjiang Lin
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. 04780v1 Announce Type: cross Abstract: Sequential Monte Carlo (SMC) methods are a natural tool for post-hoc conditioning of pretrained generative models, but in many applications the mutation kernels used by the particle system are biased approximations of an ideal Feynman--Kac flow.
By Stanislas Strasman (SU, LPSM), Gabriel Victorino Cardoso (LPSM), Sylvain Le Corff (LPSM), Vincent Lemaire (LPSM), Antonio Ocello
arXiv:2609. 01166v1 Announce Type: cross Abstract: The present research is devoted to the nonparametric estimation of a density-dependent drift coefficient in a multivariate McKean--Vlasov diffusion from independent observations at a common time, as well as the stationary density.
By Denis Belomestny, Ekaterina Morozova