Abstract
Recent advances in generative modelling have introduced powerful techniques for high-fidelity data synthesis. Modern generative approaches, including autoregressive models, generative adversarial networks, variational autoencoders, flow models, and diffusion models, enable the generation of data samples from unknown distributions, effectively addressing challenges in data simulation. However, these techniques typically require substantial computational resources, such as multiple high-performance GPUs and prolonged training time, to achieve state-of-the-art performance on high-dimensional data such as text, images, and 3D content.In this thesis, I introduce a novel perspective that theoretically establishes an efficient learning framework for generative modelling to address this difficulty. In particular, generative modelling can be viewed as learning a transport map (or plan) between a base measure μ and a target measure ν. Modern generative models treat μ and ν as two fixed ends, which is referred to as the fixed-end generative system in this work. The base end μ of this fixed-end system is typically the standard Gaussian. The proposed perspective considers the fixed base end μ as a flexible end, where the perturbation of μ is allowed by exploring a family of probability measures. This enables us to replace μ with a "better" base measure ω, thereby achieving a lower energy of the underlying generative system by exploring the space of a given family of probability measures. Therefore, we can learn the transport from ω to ν with less effort than from μ to ν. The proposed general and efficient learning framework for generative modelling, built upon this idea, is called Base Initialization (BI).
This thesis is organised into three parts. The first part presents the theoretical formulation of the fixed-end generative system, equipped with a free base end, which is referred to as the base-end free-able generative system. In particular, to analyse the properties of this new system, I generalise the classical Monge-Kantorovich problem into a relaxed Monge-Kantorovich problem. The existence and uniqueness of the solutions to this relaxed problem are investigated. In the second part, I propose the Base Initialisation framework, derived from the theoretical results under the relaxed Monge-Kantorovich formulation, and present prototype implementations of this framework. The third part demonstrates the effectiveness of the Base Initialisation framework in improving the learning efficiency of generative modelling on both 2D and 3D generation tasks.
| Date of Award | 10 Dec 2025 |
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| Original language | English |
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| Supervisor | Wenbin Li (Supervisor) & Yongliang Yang (Supervisor) |