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In this paper, we study the problem of learning multi-dimensional Gaussian Mixture Models (GMMs), with a specific focus on model order selection and efficient mixing distribution estimation. We first establish an information-theoretic lower…

Diffusion-based generative models are extremely effective in generating high-quality images, with generated samples often surpassing the quality of those produced by other models under several metrics. One distinguishing feature of these…

Denoising Diffusion Probabilistic Models (DDPMs) have emerged as a powerful family of generative models that can yield high-fidelity samples and competitive log-likelihoods across a range of domains, including image and speech synthesis.…

Mammography is the most commonly used imaging modality for breast cancer screening, driving an increasing demand for deep-learning techniques to support large-scale analysis. However, the development of accurate and robust methods is often…

While deep neural networks (NN) significantly advance image compressed sensing (CS) by improving reconstruction quality, the necessity of training current CS NNs from scratch constrains their effectiveness and hampers rapid deployment.…

Hyperspectral unmixing while considering endmember variability is usually performed by the normal compositional model (NCM), where the endmembers for each pixel are assumed to be sampled from unimodal Gaussian distributions. However, in…

Recent advances in generative modeling with diffusion processes (DPs) enabled breakthroughs in image synthesis. Despite impressive image quality, these models have various prompt compliance problems, including low recall in generating…

Restricted Boltzmann machines (RBMs) and their extensions, called 'deep-belief networks', are powerful neural networks that have found applications in the fields of machine learning and artificial intelligence. The standard way to training…

Reverse sampling and score-distillation have emerged as main workhorses in recent years for image manipulation using latent diffusion models (LDMs). While reverse diffusion sampling often requires adjustments of LDM architecture or feature…

Gaussian processes (GPs) are flexible models that can capture complex structure in large-scale dataset due to their non-parametric nature. However, the usage of GPs in real-world application is limited due to their high computational cost…

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…

Diffusion Probabilistic Models (DPMs) have emerged as the de facto approach for high-fidelity image synthesis, operating diffusion processes on continuous VAE latent, which significantly differ from the text generation methods employed by…

Data compression is a critical technology for large-scale plasma simulations. Storing complete particle information requires Terabyte-scale data storage, and analysis requires ad-hoc scalable post-processing tools. We propose a…

Accurate learning of system dynamics is becoming increasingly crucial for advanced control and decision-making in engineering. However, real-world systems often exhibit multiple channels and highly nonlinear transition dynamics, challenging…

Inverse design refers to the problem of optimizing the input of an objective function in order to enact a target outcome. For many real-world engineering problems, the objective function takes the form of a simulator that predicts how the…

We introduce the Fixed Point Diffusion Model (FPDM), a novel approach to image generation that integrates the concept of fixed point solving into the framework of diffusion-based generative modeling. Our approach embeds an implicit fixed…

We present a concise, self-contained derivation of diffusion-based generative models. Starting from basic properties of Gaussian distributions (densities, quadratic expectations, re-parameterisation, products, and KL divergences), we…

Seismic imaging from sparsely acquired data faces challenges such as low image quality, discontinuities, and migration swing artifacts. Existing convolutional neural network (CNN)-based methods struggle with complex feature distributions…

Saddle point search schemes are widely used to identify the transition state of different processes, like chemical reactions, surface and bulk diffusion, surface adsorption, and many more. In solid-state materials with relatively large…

Denoising Diffusion Probabilistic Models (DDPMs) have gained great attention in adversarial purification. Current diffusion-based works focus on designing effective condition-guided mechanisms while ignoring a fundamental problem, i.e., the…