Related papers: DEGMC: Denoising Diffusion Models Based on Riemann…

Recently, machine learning methods have gained significant traction in scientific computing, particularly for solving Partial Differential Equations (PDEs). However, methods based on deep neural networks (DNNs) often lack convergence…

We focus on the problem of efficient sampling and learning of probability densities by incorporating symmetries in probabilistic models. We first introduce Equivariant Stein Variational Gradient Descent algorithm -- an equivariant sampling…

The Euclidean scattering transform was introduced nearly a decade ago to improve the mathematical understanding of convolutional neural networks. Inspired by recent interest in geometric deep learning, which aims to generalize convolutional…

Modern machine learning increasingly leverages the insight that high-dimensional data often lie near low-dimensional, non-linear manifolds, an idea known as the manifold hypothesis. By explicitly modeling the geometric structure of data…

We present DeepFDM, a differentiable finite-difference framework for learning spatially varying coefficients in time-dependent partial differential equations (PDEs). By embedding a classical forward-Euler discretization into a convolutional…

Recent advances in imaging and high-performance computing have made it possible to image the entire human brain at the cellular level. This is the basis to study the multi-scale architecture of the brain regarding its subdivision into brain…

Computational imaging is crucial in many disciplines from autonomous driving to life sciences. However, traditional model-driven and iterative methods consume large computational power and lack scalability for imaging. Deep learning (DL) is…

Denoising diffusion models have recently emerged as the predominant paradigm for generative modelling on image domains. In addition, their extension to Riemannian manifolds has facilitated a range of applications across the natural…

Denoising Diffusion Probabilistic Models (DDPMs) have achieved impressive performance on various generation tasks. By modeling the reverse process of gradually diffusing the data distribution into a Gaussian distribution, generating a…

Despite the success of diffusion models (DMs), we still lack a thorough understanding of their latent space. While image editing with GANs builds upon latent space, DMs rely on editing the conditions such as text prompts. We present an…

To generate data from trained diffusion models, most inference algorithms, such as DDPM, DDIM, and other variants, rely on discretizing the reverse SDEs or their equivalent ODEs. In this paper, we view such approaches as decomposing the…

Incorporating group symmetries via equivariance into neural networks has emerged as a robust approach for overcoming the efficiency and data demands of modern deep learning. While most existing approaches, such as group convolutions and…

Recent works have shown that diffusion models can learn essentially any distribution provided one can perform score estimation. Yet it remains poorly understood under what settings score estimation is possible, let alone when practical…

Diffusion probabilistic models (DPMs), widely recognized for their potential to generate high-quality samples, tend to go unnoticed in representation learning. While recent progress has highlighted their potential for capturing visual…

Molecular dynamics (MD) has long been the de facto choice for simulating complex atomistic systems from first principles. Recently deep learning models become a popular way to accelerate MD. Notwithstanding, existing models depend on…

Light microscopy is a widespread and inexpensive imaging technique facilitating biomedical discovery and diagnostics. However, light diffraction barrier and imperfections in optics limit the level of detail of the acquired images. The…

Automatic layout generation that can synthesize high-quality layouts is an important tool for graphic design in many applications. Though existing methods based on generative models such as Generative Adversarial Networks (GANs) and…

Score-based diffusion models, which generate new data by learning to reverse a diffusion process that perturbs data from the target distribution into noise, have achieved remarkable success across various generative tasks. Despite their…

Sodium MRI is an imaging technique used to visualize and quantify sodium concentrations in vivo, playing a role in many biological processes and potentially aiding in breast cancer characterization. Sodium MRI, however, suffers from…

This paper explores the characterization of equivariant linear layers for representations of permutations and related groups. Unlike traditional approaches, which address these problems using parameter-sharing, we consider an alternative…