Related papers: Heavy-Tailed Diffusion with Denoising L\'evy Proba…
Symmetric positive definite~(SPD) matrices have shown important value and applications in statistics and machine learning, such as FMRI analysis and traffic prediction. Previous works on SPD matrices mostly focus on discriminative models,…
In this paper, a signal detection method based on the denoise diffusion model (DM) is proposed, which outperforms the maximum likelihood (ML) estimation method that has long been regarded as the optimal signal detection technique.…
Modelling extreme events and heavy-tailed phenomena is central to building reliable predictive systems in domains such as finance, climate science, and safety-critical AI. While L\'evy processes provide a natural mathematical framework for…
Due to the dynamics of underlying physics and external influences, the uncertainty of time series often varies over time. However, existing Denoising Diffusion Probabilistic Models (DDPMs) often fail to capture this non-stationary nature,…
A prominent family of methods for learning data distributions relies on density ratio estimation (DRE), where a model is trained to $\textit{classify}$ between data samples and samples from some reference distribution. DRE-based models can…
Although large language models (LLMs) have achieved significant success, their vulnerability to adversarial perturbations, including recent jailbreak attacks, has raised considerable concerns. However, the increasing size of these models…
Through Diffusion Models (DMs), we have made significant advances in generating high-quality images. Our exploration of these models delves deeply into their core operational principles by systematically investigating key aspects across…
Recent theoretical studies have shown that heavy-tails can emerge in stochastic optimization due to `multiplicative noise', even under surprisingly simple settings, such as linear regression with Gaussian data. While these studies have…
Interpreting EEG signals linked to spoken language presents a complex challenge, given the data's intricate temporal and spatial attributes, as well as the various noise factors. Denoising diffusion probabilistic models (DDPMs), which have…
Large Language Models (LLMs) have demonstrated remarkable capabilities in code generation. However, the quality of the generated code is heavily dependent on the structure and composition of the prompts used. Crafting high-quality prompts…
This paper introduces Discrete Markov Probabilistic Models (DMPMs), a novel discrete diffusion algorithm for discrete data generation. The algorithm operates in discrete bit space, where the noising process is a continuous-time Markov chain…
We study the distributed stochastic optimization (DSO) problem under a heavy-tailed noise condition by utilizing a multi-agent system. Despite the extensive research on DSO algorithms used to solve DSO problems under light-tailed noise…
In data-driven drug discovery, designing molecular descriptors is a very important task. Deep generative models such as variational autoencoders (VAEs) offer a potential solution by designing descriptors as probabilistic latent vectors…
Analysis of galaxy--galaxy strong lensing systems is strongly dependent on any prior assumptions made about the appearance of the source. Here we present a method of imposing a data-driven prior / regularisation for source galaxies based on…
Diffusion models excel at image restoration via probabilistic modeling of forward noise addition and reverse denoising, and their ability to handle complex noise while preserving fine details makes them well-suited for Low-Light Image…
A diffusion probabilistic model (DPM), which constructs a forward diffusion process by gradually adding noise to data points and learns the reverse denoising process to generate new samples, has been shown to handle complex data…
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…
Tweedie distributions are a special case of exponential dispersion models, which are often used in classical statistics as distributions for generalized linear models. Here, we reveal that Tweedie distributions also play key roles in modern…
We provide theoretical convergence guarantees for score-based generative models (SGMs) such as denoising diffusion probabilistic models (DDPMs), which constitute the backbone of large-scale real-world generative models such as DALL$\cdot$E…
In this paper, conditional denoising diffusion probabilistic models (DDPMs) are proposed to enhance the data transmission and reconstruction over wireless channels. The underlying mechanism of DDPM is to decompose the data generation…