Related papers: GRIFDIR: Graph Resolution-Invariant FEM Diffusion …

We propose a representation of graph as a functional object derived from the power iteration of the underlying adjacency matrix. The proposed functional representation is a graph invariant, i.e., the functional remains unchanged under any…

Using diffusion models to solve inverse problems is a growing field of research. Current methods assume the degradation to be known and provide impressive results in terms of restoration quality and diversity. In this work, we leverage the…

A novel global energy model for multi-class semantic image segmentation is proposed that admits very efficient exact inference and derivative calculations for learning. Inference in this model is equivalent to MAP inference in a particular…

Recently deep neutral networks have achieved promising performance for filling large missing regions in image inpainting tasks. They usually adopted the standard convolutional architecture over the corrupted image, leading to meaningless…

Domain generalization (DG) for object detection aims to enhance detectors' performance in unseen scenarios. This task remains challenging due to complex variations in real-world applications. Recently, diffusion models have demonstrated…

Numerical modeling of wave propagation in heterogeneous media is important in many applications. Due to the complex nature, direct numerical simulations on the fine grid are prohibitively expensive. It is therefore important to develop…

Image generation models trained on large datasets can synthesize high-quality images but often produce spatially inconsistent and distorted images due to limited information about the underlying structures and spatial layouts. In this work,…

In many environmental applications involving spatially-referenced data, limitations on the number and locations of observations motivate the need for practical and efficient models for spatial interpolation, or kriging. A key component of…

Graph foundation models (GFMs) seek transferable representations across graph domains but are limited by structural heterogeneity and incompatible node feature spaces. We propose Structure-Centric Graph Foundation Models (SCGFM), which…

3D reconstruction from a single image is a long-standing problem in computer vision. Learning-based methods address its inherent scale ambiguity by leveraging increasingly large labeled and unlabeled datasets, to produce geometric priors…

We introduce an (equi-)affine invariant diffusion geometry by which surfaces that go through squeeze and shear transformations can still be properly analyzed. The definition of an affine invariant metric enables us to construct an invariant…

The success of denoising diffusion models in representing rich data distributions over 2D raster images has prompted research on extending them to other data representations, such as vector graphics. Unfortunately due to their variable…

We consider core-periphery structured graphs, which are graphs with a group of densely and sparsely connected nodes, respectively, referred to as core and periphery nodes. The so-called core score of a node is related to the likelihood of…

The existing methods learn geographic network representations through deep graph neural networks (GNNs) based on the i.i.d. assumption. However, the spatial heterogeneity and temporal dynamics of geographic data make the out-of-distribution…

While working within the spatial domain can pose problems associated with ill-conditioned scores caused by power-law decay, recent advances in diffusion-based generative models have shown that transitioning to the wavelet domain offers a…

In this paper, we study the partial differential equation models of neural networks. Neural network can be viewed as a map from a simple base model to a complicate function. Based on solid analysis, we show that this map can be formulated…

Recent advances in generative modeling, namely Diffusion models, have revolutionized generative modeling, enabling high-quality image generation tailored to user needs. This paper proposes a framework for the generative design of structural…

Neural operators aim to learn mappings between infinite-dimensional function spaces, but their performance often degrades on complex or irregular geometries due to the lack of geometry-aware representations. We propose the Finite Element…

This paper introduces a novel graph signal processing framework for building graph-based models from classes of filtered signals. In our framework, graph-based modeling is formulated as a graph system identification problem, where the goal…

Diffusion models have recently emerged as powerful generative models in medical imaging. However, it remains a major challenge to combine these data-driven models with domain knowledge to guide brain imaging problems. In neuroimaging,…