arXiv:2608. 19067v1 Announce Type: cross Abstract: The empirical success of diffusion models in generative modelling has motivated theoretical work, including quantitative error bounds and qualitative analyses that characterise the different phases of denoising.
arXiv:2409. 18804v3 Announce Type: replace-cross Abstract: Denoising Diffusion Probabilistic Models (DDPM) are powerful state-of-the-art methods used to generate synthetic data from high-dimensional data distributions and are widely used for image, audio, and video generation as well as many more applications in science and beyond.
arXiv:2409. 02426v5 Announce Type: replace Abstract: Despite their empirical success across a wide range of generative tasks, the fundamental principles underlying the ability of diffusion models to learn data distributions are poorly understood.
arXiv:2607. 21847v1 Announce Type: cross Abstract: We introduce the distributional determinantal point process (dDPP) as a novel repulsive point process whose atoms are probability distributions rather than points in a real space.
arXiv:2405. 15768v2 Announce Type: replace-cross Abstract: In this paper, we address the classification of instances represented by distributions on a vector space rather than single points.
arXiv:2606. 19894v1 Announce Type: new Abstract: The remarkable success of score-based diffusion models has spurred significant efforts to establish their theoretical foundations.
arXiv:2501. 12982v3 Announce Type: replace-cross Abstract: This paper investigates how diffusion generative models leverage (unknown) low-dimensional structure to accelerate sampling.
arXiv:2608. 08704v1 Announce Type: cross Abstract: Kernel spectral clustering with a single bandwidth can be inadequate for data exhibiting multiple characteristic pairwise-distance scales, a problem particularly prevalent in the high-dimensional regime.
arXiv:2510. 12744v2 Announce Type: replace-cross Abstract: We develop a unified statistical framework for softmax-gated Gaussian mixture of experts (SGMoE) that addresses three long-standing obstacles in parameter estimation and model selection: (i) non-identifiability of gating parameters up to common translations, (ii) intrinsic gate-expert interactions that induce coupled differential relations in the likelihood, and (iii) the tight numerator-denominator coupling in the softmax-induced conditional density.
arXiv:2411. 12438v2 Announce Type: replace-cross Abstract: We develop a new approach for clustering non-spherical (i.
arXiv:2509. 22879v2 Announce Type: replace-cross Abstract: Mixture models, such as Gaussian mixture models, are widely used in machine learning to represent complex data distributions.
arXiv:2512. 04954v3 Announce Type: replace Abstract: We present a novel technique for amortized posterior estimation using Normalizing Flows trained with likelihood-weighted importance sampling.
arXiv:2606. 03212v1 Announce Type: new Abstract: Low-rank tensor decomposition (TD) is usually effective on clean, fully observed data, but it often degrades under severe missingness or noise.