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This dissertation attempts to drive innovation in the field of generative modeling for computer vision, by exploring novel formulations of conditional generative models, and innovative applications in images, 3D animations, and video. Our…

Poroelasticity -- coupled fluid flow and elastic deformation in porous media -- often involves spatially variable permeability, especially in subsurface systems. In such cases, simulations with random permeability fields are widely used for…

Surrogate strategies are used widely for uncertainty quantification of groundwater models in order to improve computational efficiency. However, their application to dynamic multiphase flow problems is hindered by the curse of…

Diffusion models (DMs) have become the dominant paradigm of generative modeling in a variety of domains by learning stochastic processes from noise to data. Recently, diffusion denoising bridge models (DDBMs), a new formulation of…

Video face restoration aims to enhance degraded face videos into high-quality results with realistic facial details, stable identity, and temporal coherence. Recent diffusion-based methods have brought strong generative priors to…

In this paper, we develop a physics-informed deep operator learning framework for solving multi-term time-fractional mixed diffusion-wave equations (TFMDWEs). We begin by deriving an $L_2$ approximation, which achieves first-order accuracy…

We propose a novel \textit{capsule} based deep encoder-decoder model for surrogate modeling and uncertainty quantification of systems in mechanics from sparse data. The proposed framework is developed by adapting Capsule Network (CapsNet)…

Conventional class-guided diffusion models generally succeed in generating images with correct semantic content, but often struggle with texture details. This limitation stems from the usage of class priors, which only provide coarse and…

Diffusion-based inpainting can reconstruct missing image areas with high quality from sparse data, provided that their location and their values are well optimised. This is particularly useful for applications such as image compression,…

Diffusion models (DMs) have revolutionized generative learning. They utilize a diffusion process to encode data into a simple Gaussian distribution. However, encoding a complex, potentially multimodal data distribution into a single…

Instructional video editing applies edits to an input video using only text prompts, enabling intuitive natural-language control. Despite rapid progress, most methods still require fixed-length inputs and substantial compute. Meanwhile,…

Diffusion models are primarily trained for image synthesis, yet their denoising trajectories encode rich, spatially aligned visual priors. In this paper, we demonstrate that these priors can be utilized for text-conditioned semantic and…

Machine learning methods, such as diffusion models, are widely explored as a promising way to accelerate high-fidelity fluid dynamics computation via a super-resolution process from faster-to-compute low-fidelity input. However, existing…

Diffusion models have demonstrated exceptional capabilities in image restoration, yet their application to video super-resolution (VSR) faces significant challenges in balancing fidelity with temporal consistency. Our evaluation reveals a…

This work aims to improve the applicability of diffusion models in realistic image restoration. Specifically, we enhance the diffusion model in several aspects such as network architecture, noise level, denoising steps, training image size,…

Latent diffusion models for medical image super-resolution universally inherit variational autoencoders designed for natural photographs. We show that this default choice, not the diffusion architecture, is the dominant constraint on…

High-fidelity simulation of complex physical systems is exorbitantly expensive and inaccessible across spatiotemporal scales. Recently, there has been an increasing interest in leveraging deep learning to augment scientific data based on…

Partial differential equations (PDEs) are fundamental to modeling complex and nonlinear physical phenomena, but their numerical solution often requires significant computational resources, particularly when a large number of forward full…

Partial differential equations (PDEs) are a central tool for modeling the dynamics of physical, engineering, and materials systems, but high-fidelity simulations are often computationally expensive. At the same time, many scientific…

The use of machine learning in fluid dynamics is becoming more common to expedite the computation when solving forward and inverse problems of partial differential equations. Yet, a notable challenge with existing convolutional neural…