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Despite their outstanding performance in a broad spectrum of real-world tasks, deep artificial neural networks are sensitive to input noises, particularly adversarial perturbations. On the contrary, human and animal brains are much less…

Diffusion models rely on a high-dimensional latent space of initial noise seeds, yet it remains unclear whether this space contains sufficient structure to predict properties of the generated samples, such as their classes. In this work, we…

Generative diffusion processes are an emerging and effective tool for image and speech generation. In the existing methods, the underline noise distribution of the diffusion process is Gaussian noise. However, fitting distributions with…

This paper investigates score-based diffusion models when the underlying target distribution is concentrated on or near low-dimensional manifolds within the higher-dimensional space in which they formally reside, a common characteristic of…

Diffusion models have recently emerged as powerful tools for missing data imputation by modeling the joint distribution of observed and unobserved variables. However, existing methods, typically based on stochastic denoising diffusion…

As a class of generative artificial intelligence frameworks inspired by statistical physics, diffusion models have shown extraordinary performance in synthesizing complicated data distributions through a denoising process gradually guided…

This work presents a diffusion transformer framework for data-driven structural topology optimization that combines the accuracy of physics-based methods with the efficiency of generative deep learning. Conventional approaches such as the…

Diffusion models (DMs) are a class of generative machine learning methods that sample a target distribution by transforming samples of a trivial (often Gaussian) distribution using a learned stochastic differential equation. In standard…

Multi-Source Diffusion Models (MSDM) allow for compositional musical generation tasks: generating a set of coherent sources, creating accompaniments, and performing source separation. Despite their versatility, they require estimating the…

Analytical diffusion models offer a mathematically transparent path to generative modeling by formulating the denoising score as an empirical-Bayes posterior mean. However, this interpretability comes at a prohibitive cost: the standard…

Diffusion models are generative models that have shown significant advantages compared to other generative models in terms of higher generation quality and more stable training. However, the computational need for training diffusion models…

Wall-bounded turbulent flows are chaotic and multiscale, rendering real-time prediction at high Reynolds numbers computationally prohibitive in applications such as wind farms. Classical data assimilation methods are based on repeated…

Climate change necessitates rapid expansion of renewable energy, with wind energy offering a scalable and low-impact solution. However, accurate prediction of wind loads and power generation remains challenging due to uncertainties in wind…

Recent advances in diffusion models attempt to handle conditional generative tasks by utilizing a differentiable loss function for guidance without the need for additional training. While these methods achieved certain success, they often…

Conditional diffusion models have the generative controllability by incorporating external conditions. However, their performance significantly degrades with noisy conditions, such as corrupted labels in the image generation or unreliable…

Diffusion models have transformed image synthesis through iterative denoising, by defining trajectories from noise to coherent data. While their capabilities are widely celebrated, a critical challenge remains unaddressed: ensuring…

Class-conditional image generation using generative adversarial networks (GANs) has been investigated through various techniques; however, it continues to face challenges such as mode collapse, training instability, and low-quality output…

Data availability remains a critical bottleneck in many deep learning applications. Large-scale datasets are often expensive to collect, curate and annotate, which can limit the scalability and applicability of supervised learning methods.…

The manifold hypothesis asserts that data of interest in high-dimensional ambient spaces, such as image data, lies on unknown low-dimensional submanifolds. Diffusion models (DMs) -- which operate by convolving data with progressively larger…

Diffusion models are capable of impressive feats of image generation with uncommon juxtapositions such as astronauts riding horses on the moon with properly placed shadows. These outputs indicate the ability to perform compositional…