Related papers: Linearized Diffusion Map
By embedding discrete representations into a continuous latent space, we can leverage continuous-space latent diffusion models to handle generative modeling of discrete data. However, despite their initial success, most latent diffusion…
Kernel mean embeddings are a popular tool that consists in representing probability measures by their infinite-dimensional mean embeddings in a reproducing kernel Hilbert space. When the kernel is characteristic, mean embeddings can be used…
We introduce diffusion geometry as a new framework for geometric and topological data analysis. Diffusion geometry uses the Bakry-Emery $\Gamma$-calculus of Markov diffusion operators to define objects from Riemannian geometry on a wide…
Latent diffusion models (LDMs) have demonstrated remarkable generative capabilities across various low-level vision tasks. However, their potential for point cloud completion remains underexplored due to the unstructured and irregular…
We present a novel kernel-based machine learning algorithm for identifying the low-dimensional geometry of the effective dynamics of high-dimensional multiscale stochastic systems. Recently, the authors developed a mathematical framework…
Dimensionality reduction (DR) plays a vital role in the visual analysis of high-dimensional data. One main aim of DR is to reveal hidden patterns that lie on intrinsic low-dimensional manifolds. However, DR often overlooks important…
We propose SymDiff, a method for constructing equivariant diffusion models using the framework of stochastic symmetrisation. SymDiff resembles a learned data augmentation that is deployed at sampling time, and is lightweight,…
Physical systems with complex unsteady dynamics, such as fluid flows, are often poorly represented by a single mean solution. For many practical applications, it is crucial to access the full distribution of possible states, from which…
Video diffusion models (VDMs) perform attention computation over the 3D spatio-temporal domain. Compared to large language models (LLMs) processing 1D sequences, their memory consumption scales cubically, necessitating parallel serving…
We introduce R2LDM, an innovative approach for generating dense and accurate 4D radar point clouds, guided by corresponding LiDAR point clouds. Instead of utilizing range images or bird's eye view (BEV) images, we represent both LiDAR and…
In this work, we consider compressible single-phase flow problems in a porous media containing a fracture. In the latter, a non-linear pressure-velocity relation is prescribed. Using a non-overlapping domain decomposition procedure, we…
We present Neumann eigenmaps (NeuMaps), a novel approach for enhancing the standard diffusion map embedding using landmarks, i.e distinguished samples within the dataset. By interpreting these landmarks as a subgraph of the larger data…
Linear Parameter Varying (LPV) Systems are a well-established class of nonlinear systems with a rich theory for stability analysis, control, and analytical response finding, among other aspects. Although there are works on data-driven…
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…
Diffusion models, as powerful generative models, have found a wide range of applications and shown great potential in solving image reconstruction problems. Some works attempted to solve MRI reconstruction with diffusion models, but these…
Deformable image registration plays an essential role in various medical image tasks. Existing deep learning-based deformable registration frameworks primarily utilize convolutional neural networks (CNNs) or Transformers to learn features…
Implicit visual knowledge in a large latent diffusion model (LLDM) pre-trained on natural images is rich and hypothetically universal to natural and medical images. To test this hypothesis from a practical perspective, we propose a novel…
Deep learning methods have played a more and more important role in hyperspectral image classification. However, the general deep learning methods mainly take advantage of the information of sample itself or the pairwise information between…
Accurate dose distribution prediction is crucial in the radiotherapy planning. Although previous methods based on convolutional neural network have shown promising performance, they have the problem of over-smoothing, leading to prediction…
Channel gain maps (CGMs) enable propagation-aware services in edge-intelligent wireless communication networks, while diffusion-based CGM construction is memory intensive for on-device training or adaptation. This letter proposes…