Related papers: Matrix moments of the diffusion tensor distributio…

In computational and applied statistics, it is of great interest to get fast and accurate calculation for the distributions of the quadratic forms of Gaussian random variables. This paper presents a novel approximation strategy that…

Photonic crystals enable fine control over light propagation at the nanoscale, and thus play a central role in the development of photonic and quantum technologies. Photonic band diagrams (BDs) are a key tool to investigate light…

Generative diffusion processes are an emerging and effective tool for image and speech generation. In the existing methods, the underline noise distribution of the diffusion process is Gaussian noise. However, fitting distributions with…

Analytical methods for finding moments of random Vandermonde matrices with entries on the unit circle are developed. Vandermonde Matrices play an important role in signal processing and wireless applications such as direction of arrival…

Diffusion Tensor Imaging (DTI) allows estimating the position, orientation and dimension of bundles of nerve pathways. This non-invasive imaging technique takes advantage of the diffusion of water molecules and determines the diffusion…

Standard diffusion models for graph generation typically rely on uniform time-stepping, an approach that overlooks the non-homogeneous dynamics of distributional evolution on complex manifolds. In this paper, we present an…

Denoising Diffusion Models (DDMs) have become a popular tool for generating high-quality samples from complex data distributions. These models are able to capture sophisticated patterns and structures in the data, and can generate samples…

We consider a collection of $n$ points in $\mathbb{R}^d$ measured at $m$ times, which are encoded in an $n \times d \times m$ data tensor. Our objective is to define a single embedding of the $n$ points into Euclidean space which summarizes…

The problem of a spatially discontinuous diffusion coefficient ($D(\boldsymbol x)$) is one that may be encountered in hydrogeologic systems due to natural geological features or as a consequence of numerical discretization of flow…

We investigate the moment estimation for an ergodic diffusion process with unknown trend coefficient. We consider nonparametric and parametric estimation. In each case, we present a lower bound for the risk and then construct an…

We consider the problem of approximating the moment generating function (MGF) of a truncated random variable in terms of the MGF of the underlying (i.e., untruncated) random variable. The purpose of approximating the MGF is to enable the…

Masked diffusion models (MDMs) have emerged as a popular research topic for generative modeling of discrete data, thanks to their superior performance over other discrete diffusion models, and are rivaling the auto-regressive models (ARMs)…

Adapting a pretrained diffusion model to new objectives at inference time remains an open problem in generative modeling. Existing steering methods suffer from inaccurate value estimation, especially at high noise levels, which biases…

With the rapid development of AIGC technologies, generative image steganography has attracted increasing attention due to its high imperceptibility and flexibility. However, existing generative steganography methods often maintain…

Diffusion Probabilistic Models (DPMs) have achieved strong generative performance, yet their inductive biases remain largely implicit. In this work, we aim to build inductive biases into the training and sampling of diffusion models to…

Diffusion models (DMs) excel in photo-realistic image synthesis, but their adaptation to LiDAR scene generation poses a substantial hurdle. This is primarily because DMs operating in the point space struggle to preserve the curve-like…

Molecular conformer generation is a fundamental task in computational chemistry. Several machine learning approaches have been developed, but none have outperformed state-of-the-art cheminformatics methods. We propose torsional diffusion, a…

Diffusion models excel in noise-to-data generation tasks, providing a mapping from a Gaussian distribution to a more complex data distribution. However they struggle to model translations between complex distributions, limiting their…

Latent Diffusion Models (LDMs) enable high-quality image synthesis while avoiding excessive compute demands by training a diffusion model in a compressed lower-dimensional latent space. Here, we apply the LDM paradigm to high-resolution…

It is highly desirable to know how uncertain a model's predictions are, especially for models that are complex and hard to understand as in deep learning. Although there has been a growing interest in using deep learning methods in…