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This paper aims to conduct a comprehensive theoretical analysis of current diffusion models. We introduce a novel generative learning methodology utilizing the Schr{\"o}dinger bridge diffusion model in latent space as the framework for…

Diffusion models have shown remarkable performance on many generative tasks. Despite recent success, most diffusion models are restricted in that they only allow linear transformation of the data distribution. In contrast, broader family of…

Generating graph-structured data is crucial in applications such as molecular generation, knowledge graphs, and network analysis. However, their discrete, unordered nature makes them difficult for traditional generative models, leading to…

Source localization is the inverse problem of graph information dissemination and has broad practical applications. However, the inherent intricacy and uncertainty in information dissemination pose significant challenges, and the ill-posed…

The open-world test dataset is often mixed with out-of-distribution (OOD) samples, where the deployed models will struggle to make accurate predictions. Traditional detection methods need to trade off OOD detection and in-distribution (ID)…

Generative diffusion models, famous for their performance in image generation, are popular in various cross-domain applications. However, their use in the communication community has been mostly limited to auxiliary tasks like data modeling…

Diffusion models have revolutionized generative modeling, enabling unprecedented realism in image and video synthesis. This success has sparked interest in leveraging their representations for visual understanding tasks. While recent works…

Diffusion models are a class of generative models that have demonstrated remarkable success in tasks such as image generation. However, one of the bottlenecks of these models is slow sampling due to the delay before the onset of trajectory…

Molecular structure elucidation from spectra is a fundamental challenge in molecular science. Conventional approaches rely heavily on expert interpretation and lack scalability, while retrieval-based machine learning approaches remain…

Forecasting over graph-structured sensor networks demands models that capture both deterministic spatial trends and stochastic variability, while remaining efficient enough for repeated inference as new observations arrive. We propose…

Graph diffusion models have emerged as state-of-the-art techniques in graph generation; yet, integrating domain knowledge into these models remains challenging. Domain knowledge is particularly important in real-world scenarios, where…

We present SinDiffusion, leveraging denoising diffusion models to capture internal distribution of patches from a single natural image. SinDiffusion significantly improves the quality and diversity of generated samples compared with…

Graph-based learned simulators have emerged as a promising approach for simulating physical systems on unstructured meshes, offering speed and generalization across diverse geometries. However, they often struggle with capturing global…

Graph generative modelling has become an essential task due to the wide range of applications in chemistry, biology, social networks, and knowledge representation. In this work, we propose a novel framework for generating graphs by adapting…

The introduction of convolutional layers greatly advanced the performance of neural networks on image tasks due to innately capturing a way of encoding and learning translation-invariant operations, matching one of the underlying symmetries…

Fractional Brownian motion (fBm) is a ubiquitous diffusion process in which the memory effects of the stochastic transport result in the mean squared particle displacement following a power law, $\langle {\Delta r}^2 \rangle \sim…

Deep neural networks (DNNs) trained for image denoising are able to generate high-quality samples with score-based reverse diffusion algorithms. These impressive capabilities seem to imply an escape from the curse of dimensionality, but…

The reconstruction of unsteady flow fields from limited measurements is a challenging and crucial task for many engineering applications. Machine learning models are gaining popularity for solving this problem due to their ability to learn…

We consider the problem of learning a graph from a finite set of noisy graph signal observations, the goal of which is to find a smooth representation of the graph signal. Such a problem is motivated by the desire to infer relational…

As one of the most popular and sought-after generative models in the recent years, diffusion models have sparked the interests of many researchers and steadily shown excellent advantage in various generative tasks such as image synthesis,…