Date of Award

Fall 1-1-2025

Document Type

Dissertation

Degree Name

Doctor of Philosophy (PhD)

Department

Applied Mathematics

First Advisor

Kluger, Yuval

Abstract

Probabilistic generative models have seen rapid adoption as algorithmic tools in a multitude of domains due to their unparalleled capacity to model and draw samples from complex high-dimensional data distributions in a wide range of modalities. At their core, these models are simply transformations that map a simple known distribution to an arbitrarily complex target distribution. As these algorithms essentially operate over measure spaces, they are inherently stochastic, and their implementational details allow their taxonomy as either explicit or implicit probabilistic models. Explicit models directly permit the evaluation of a likelihood function p?(x), which is directly maximized with respect to ? during training. Implicit models do not permit such a computation, and are thus trained via surrogate objectives such as adversarial losses. The development of generative models traces back to algorithms such as naive Bayes, mixture models, Markov random fields, Boltzmann machines, latent Dirichlet allocation, and other classical probabilistic methods. While effective for specific tasks, these earlier models were limited in their capacity to handle the complexity of generally unstructured large-scale data. The recent leap in generative modeling is often attributed to two primary factors: the explosion of available online data and the development of GPU-accelerated computing. These have enabled the creation of massive neural network-based models with billions of parameters, capable of learning highly abstract and complex data representations. At large data and computational scale, the increasing sophistication of these models allows them to capture complex data interactions that exceed the capabilities of traditional supervised learning in a number of fundamental tasks. However, this surge in complexity has come at the cost of mathematical tractability and interpretability. Deep neural networks are often described as ”black boxes,” lacking a comprehensive theoretical understanding of their internal mechanisms and optimization dynamics. This opacity raises concerns regarding the privacy, safety, correctness, bias, and reliability of AI systems as their adoption becomes more widespread. The problem is highlighted by known vulnerabilities, such as adversarial attacks that can cause models to fail catastrophically or jailbreaking that can bypass safety guardrails. Consequently, there is an urgent and growing need for the development of more interpretable deep generative models. Achieving this requires a deliberate approach to the entire model lifecycle—from architectural design to training and evaluation—and ensure that these technologies are more secure, transparent, and controllable. In this dissertation, we take steps toward improving the interpretability and steerability of deep generative models, with a primary focus on diffusion-based algorithms. We tackle this via many different approaches, such as by deriving computationally tractable likelihood functions in cases where they are not available, designing training algorithms that improve the text-following performance of fine-tuned models, and developing inference-time algorithms for guiding diffusion processes by drawing connections to the theory of optimal control. Ultimately, we hope that the insights provided here can improve the safety, predictability, and steerability of deep generative models, and work towards justifying the investment and deployment of these algorithms across different settings in the science, technology, and creative application areas.

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