The paper investigates how many spectral directions a truncated diffusion sampler must retain when data exhibit power‑law covariance spectra. For Gaussian data compared to a smoothed target, it establishes matching upper and lower bounds on the necessary number of retained directions, assuming a sufficiently large ambient dimension. The analysis shows that truncation error depends on the combined Wiener gains of omitted directions, meaning that even weak individual directions can collectively contribute significant error, and it provides practical guidelines for selecting the retained subspace and diffusion noise level.
arXiv:2605.08392v2 Announce Type: replace Abstract: Practical diffusion sampling requires simulating a reverse-time ODE or SDE with a limited number of denoising steps, making the choice of sampling...
The paper establishes the first polynomial lower bounds on the number of parallel rounds required for diffusion sampling with approximate scores. It proves a “~Ω(d^{1/3})” lower bound for sampling smooth, near‑isotropic Gaussian mixtures in ℝ^d, and an Ω(d) lower bound for uniform sampling from anisotropic axis‑aligned boxes inside the unit ball. These bounds apply to any randomized algorithm that can make polynomially many queries per round at arbitrary locations and noise levels, while maintaining inverse‑polynomial score error and constant total variation accuracy.
arXiv:2605. 13175v2 Announce Type: replace Abstract: Recent works have proposed incorporating heavy-tailed (HT) noise into diffusion- and flow-based generative models, with the goals of better recovering the tails of target distributions and improving generative diversity.
arXiv:2603.19657v2 Announce Type: replace-cross Abstract: We study model-order selection and component-mean estimation for multidimensional Gaussian mixture models with a known common covariance matr...
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:2610. 12052v1 Announce Type: cross Abstract: Despite their empirical success, why diffusion models overcome the bottlenecks of classical score-based samplers remains unclear.
arXiv:2606. 27298v1 Announce Type: cross Abstract: We study the fundamental problem of learning a high-dimensional Gaussian truncated to an unknown halfspace.
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:2404.12613v4 Announce Type: replace-cross Abstract: In this paper, we study the problem of learning one-dimensional Gaussian mixture models (GMMs) with a specific focus on estimating both the m...
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.
arXiv:2501. 12982v3 Announce Type: replace-cross Abstract: This paper investigates how diffusion generative models leverage (unknown) low-dimensional structure to accelerate sampling.
arXiv:2610. 19692v1 Announce Type: new Abstract: Gaussian diffusion models offer a practical framework for generative modeling.