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Denoising Diffusion Probabilistic Models (DDPM) have recently gained significant attention. DDPMs compose a Markovian process that begins in the data domain and gradually adds noise until reaching pure white noise. DDPMs generate…

Statistical regression models whose mean functions are represented by ordinary differential equations (ODEs) can be used to describe phenomenons dynamical in nature, which are abundant in areas such as biology, climatology and genetics. The…

Diffusion-based generative models learn to iteratively transfer unstructured noise to a complex target distribution as opposed to Generative Adversarial Networks (GANs) or the decoder of Variational Autoencoders (VAEs) which produce samples…

Diffusion models are often trained in low-dimensional latent spaces, which are then reused for related but shifted datasets. In this work, we study when such latent reuse remains reliable under distribution shift. We consider a…

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…

Diffusion Models (DMs) utilize an iterative denoising process to transform random noise into synthetic data. Initally proposed with a UNet structure, DMs excel at producing images that are virtually indistinguishable with or without…

Diffusion models have shown strong performance in generating high-quality tabular data, but they carry privacy risks by reproducing exact training samples. While prior work focuses on dataset-level augmentation to reduce memorization,…

Latent Diffusion models (LDMs) have achieved remarkable results in synthesizing high-resolution images. However, the iterative sampling process is computationally intensive and leads to slow generation. Inspired by Consistency Models (song…

Diffusion models (DMs) create samples from a data distribution by starting from random noise and iteratively solving a reverse-time ordinary differential equation (ODE). Because each step in the iterative solution requires an expensive…

Machine Unlearning allows participants to remove their data from a trained machine learning model in order to preserve their privacy, and security. However, the machine unlearning literature for generative models is rather limited. The…

Diffusion Models enable realistic image generation, raising the risk of misinformation and eroding public trust. Currently, detecting images generated by unseen diffusion models remains challenging due to the limited generalization…

Generative models have recently revolutionized image generation tasks across diverse domains, including galaxy image synthesis. This study investigates the statistical learning and consistency of three generative models: light-weight-gan (a…

Evidence accumulation models of simple decision-making have long assumed that the brain estimates a scalar decision variable corresponding to the log-likelihood ratio of the two alternatives. Typical neural implementations of this…

Diffusion models have achieved unprecedented performance in generative modeling. The commonly-adopted formulation of the latent code of diffusion models is a sequence of gradually denoised samples, as opposed to the simpler (e.g., Gaussian)…

Diffusionmodels(DMs)havedemonstratedremarkableachievements in synthesizing images of high fidelity and diversity. However, the extensive computational requirements and slow generative speed of diffusion models have limited their widespread…

Diffusion Models (DMs) have demonstrated state-of-the-art performance in content generation without requiring adversarial training. These models are trained using a two-step process. First, a forward - diffusion - process gradually adds…

AI models present a wide range of applications in the field of medicine. However, achieving optimal performance requires access to extensive healthcare data, which is often not readily available. Furthermore, the imperative to preserve…

Real-world datasets are inherently heterogeneous, yet how per-class structural differences and sampling imbalance shape the training dynamics of diffusion models-and potentially exacerbate disparities-remains poorly understood. While models…

Denoising diffusion models have emerged as a dominant approach for image generation, however they still suffer from slow convergence in training and color shift issues in sampling. In this paper, we identify that these obstacles can be…

Diffusion models have become the de facto framework for generating new datasets. The core of these models lies in the ability to reverse a diffusion process in time. The goal of this manuscript is to explain, from a PDE perspective, how…