| Author: | Huang, Ding |
| Title: | Diffusion and interpolation-based conditional generative models : theoretical analysis and applications |
| Advisors: | Li, Ting (AMA) Huang, Jian (DSAI) Jiang, Binyan (DSAI) |
| Degree: | Ph.D. |
| Year: | 2026 |
| Subject: | Deep learning (Machine learning) Neural networks (Computer science) Mathematical statistics Hong Kong Polytechnic University -- Dissertations |
| Department: | Department of Applied Mathematics |
| Pages: | xviii, 241 pages : color illustrations |
| Language: | English |
| Abstract: | Recent advances in deep generative learning have enabled powerful new approaches for statistical modeling, with the conditional generative paradigm in particular serving as a highly scalable tool for quantifying complex relationships in high-dimensional data. Within this domain, process-based methods, such as diffusion and interpolation models, have emerged as the state-of-the-art. However, significant theoretical and practical challenges remain. This dissertation addresses these critical issues across the spectrum of theory, methodology, and scientific application to advance the capabilities of process-based conditional generation. First, we construct a rigorous theoretical foundation for this model class. We introduce the Conditional Stochastic Interpolation (CSI) framework, which provides a unified mathematical treatment for both Ordinary Differential Equation (ODE) and Stochastic Differential Equation (SDE) based samplers. In our proposed approach, we incorporate an adaptive diffusion term to address the instability issues arising in the diffusion process. We derive explicit expressions of the conditional drift and score functions in terms of conditional expectations, which naturally lead to an nonparametric regression approach to estimating these functions. Furthermore, we establish nonasymptotic error bounds for learning the target conditional distribution. This work provides robust and versatile learning guarantees for a broad class of models. Second, we address the practical challenge of adapting large, pre-trained diffusion models to new domains. We propose a Bayesian finetuning framework that treats the pre-trained score function as a prior and updates it using task-specific information. We implement this through a novel, parameter-efficient neural network architecture called Bayesian Power Steering (BPS), which demonstrates exceptional performance in data-scarce conditional image generation tasks by operating on the model's hierarchical feature spaces. Notably, BPS attains an FID score of 10.49 under the sketch condition on the COCO17 dataset. Finally, we apply these principles to a critical problem in computational biology: modeling single-cell gene expression data. We develop a novel cross-dataset conditional diffusion model that integrates heterogeneous single-cell datasets to predict gene expressions. By incorporating adaptive normalization and graph attention-based interaction modeling, our framework learns a shared representation of gene expression that leverages large public atlases to improve generation quality for small target datasets. Our model achieves state-of-the-art performance, demonstrating its potential to accelerate experimental design and therapeutic discovery. |
| Rights: | All rights reserved |
| Access: | open access |
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