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.
arXiv:2607. 07967v1 Announce Type: cross Abstract: Diffusion-based policies have recently emerged as powerful policy parameterizations for reinforcement learning, representing state-conditioned action distributions as terminal laws of diffusion processes with parameterized drifts.
arXiv:2610.22693v1 Announce Type: cross Abstract: We study uniform approximation of the H\"older ball $\mathcal H_1^s([0,1]^D)$ by fully connected ReLU networks. Except in the one-dimensional Lipschi...
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.
arXiv:2606. 03820v1 Announce Type: cross Abstract: We develop a quantitative approximation framework for diffusion distillation, viewing few-step sampling as error propagation under compositions of learned flow maps.
The paper introduces a new optimal transport framework that uses the Barron energy—an intrinsic neural network complexity measure—instead of the traditional kinetic energy. By modeling transport as deep residual networks that map a reference distribution to a target distribution, the authors define a new metric on probability measures and analyze its properties for generative modeling. They demonstrate that diffusion generative models are suboptimal in this Barron geometry and explore how adaptivity can improve alternative generative approaches.
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.
arXiv:2607. 23226v1 Announce Type: new Abstract: Despite the empirical success of score-based diffusion models, a complete theoretical understanding of how finite-sample learning, network parameterization, and numerical discretization jointly dictate generative quality remains underdeveloped.
arXiv:2601.20250v2 Announce Type: replace Abstract: Recently, flow-based generative models have shown superior efficiency compared to diffusion models. In this paper, we study rectified flow models,...
arXiv:2610.02253v1 Announce Type: new Abstract: The universal approximation property of dropout neural networks does not by itself describe the network size required for an accurate random realizatio...
arXiv:2608. 18237v1 Announce Type: cross Abstract: Estimating the difference of two Stein's score functions is a fundamental problem in generative modeling.
The paper presents sample complexity bounds for sampling high‑dimensional categorical distributions with local dependence using discrete diffusions. It introduces a pinning decomposition of the discrete score, enabling a weight‑sharing neural score learner combined with τ‑leaping for efficient end‑to‑end sampling. The authors derive explicit guarantees that depend on vocabulary size, MRF interaction order, and sample size, and demonstrate that weight‑sharing networks outperform fully connected ones on Potts, Ising, and tree‑structured models.