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Autoregressive models are structurally misaligned with the inherently parallel nature of geospatial understanding, forcing a rigid sequential narrative onto scenes and fundamentally hindering the generation of structured and coherent…

Extensive pre-training with large data is indispensable for downstream geometry and semantic visual perception tasks. Thanks to large-scale text-to-image (T2I) pretraining, recent works show promising results by simply fine-tuning T2I…

3D brain MRI studies often examine subtle morphometric differences between cohorts that are hard to detect visually. Given the high cost of MRI acquisition, these studies could greatly benefit from image syntheses, particularly…

Joint modeling of spatially-oriented dependent variables is commonplace in the environmental sciences, where scientists seek to estimate the relationships among a set of environmental outcomes accounting for dependence among these outcomes…

Score-based diffusion models provide a powerful way to model images using the gradient of the data distribution. Leveraging the learned score function as a prior, here we introduce a way to sample data from a conditional distribution given…

Point pattern data often exhibit features such as abrupt changes, hotspots and spatially varying dependence in local intensity. Under a Poisson process framework, these correspond to discontinuities and nonstationarity in the underlying…

Spatio-temporal data abounds in domain like traffic and environmental monitoring. However, it often suffers from missing values due to sensor malfunctions, transmission failures, etc. Recent years have seen continued efforts to improve…

Diffusion models are at the vanguard of generative AI research with renowned solutions such as ImageGen by Google Brain and DALL.E 3 by OpenAI. Nevertheless, the potential merits of diffusion models for communication engineering…

Models which include domain constraints occur in myriad contexts such as econometrics, genomics, and environmetrics, though simulating from constrained distributions can be computationally expensive. In particular, repeated sampling from…

Tractography is typically performed for each subject using the diffusion tensor imaging (DTI) data in its native subject space rather than in some space common to the entire study cohort. Despite performing tractography on a population…

This thesis focuses on data that has complex spatio-temporal structure and on probabilistic graphical models that learn the structure in an interpretable and scalable manner. We target two research areas of interest: Gaussian graphical…

Probabilistic forecasting is crucial for real-world spatiotemporal systems, such as climate, energy, and urban environments, where quantifying uncertainty is essential for informed, risk-aware decision-making. While diffusion models have…

Graphical models are widely used in diverse application domains to model the conditional dependencies amongst a collection of random variables. In this paper, we consider settings where the graph structure is covariate-dependent, and…

Poor performance of quantitative analysis in histopathological Whole Slide Images (WSI) has been a significant obstacle in clinical practice. Annotating large-scale WSIs manually is a demanding and time-consuming task, unlikely to yield the…

We investigate the approximation efficiency of score functions by deep neural networks in diffusion-based generative modeling. While existing approximation theories utilize the smoothness of score functions, they suffer from the curse of…

Most brain disorders are very heterogeneous in terms of their underlying biology and developing analysis methods to model such heterogeneity is a major challenge. A promising approach is to use probabilistic regression methods to estimate…

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…

We develop a Bayesian bivariate spatial model for multivariate regression analysis applicable to studies examining the influence of genetic variation on brain structure. Our model is motivated by an imaging genetics study of the Alzheimer's…

Diffusion probabilistic models have quickly become a major approach for generative modeling of images, 3D geometry, video and other domains. However, to adapt diffusion generative modeling to these domains the denoising network needs to be…

Diffusion geometry is a manifold learning framework that uses random walks defined by Markov transition matrices to characterize the geometry of a dataset at multiple scales. We use diffusion geometry for neural representations,…