<p><em>Image-to-image regression is an important computer vision research topic. Previous</em></p> <p><em>research works have been concentrating on task-dependent end-to-end regression models. In</em></p> <p><em>this dissertation, we focus on a generative regression framework based on score matching.</em></p> <p><em>Such generative models are called score-based generative models, which learn the data score</em></p> <p><em>functions by gradually adding noise to data using a diffusion process. Images can be generated</em></p> <p><em>with learned score functions through a time-reversal sampling process.</em></p> <p><em>First, we propose a conditional score matching regression framework which targets the</em></p> <p><em>conditional score functions in regression problems. The framework can perform diverse inferences</em></p> <p><em>about conditional distribution by generating samples. We demonstrate its advantages</em></p> <p><em>with various image-to-image regression applications.</em></p> <p><em>Second, we propose a score-based regression model that applies the diffusion process to</em></p> <p><em>both input and response images simultaneously. The proposed method, called synchronized</em></p> <p><em>diffusion, can help stabilize model parameter learning and increase model robustness. In</em></p> <p><em>addition, we develop an effective prediction algorithm based on the Expectation-Maximization</em></p> <p><em>(EM) algorithm which can improve accuracy and computation speed. We illustrate the efficacy</em></p> <p><em>of our proposed approach on high-resolution image datasets.</em></p> <p><em>The last part of the dissertation focuses on analyzing the score-based generative modeling</em></p> <p><em>framework. We conduct a theoretical analysis of the variance exploding behavior observed in</em></p> <p><em>training score-based generative models with denoising score matching objective functions. We</em></p> <p><em>explain the large variance problem from a nonparametric estimation perspective. Furthermore,</em></p> <p><em>we propose a solution to the general score function estimation problem based on Simulation-</em></p> <p><em>Extrapolation (SIMEX), which was originally developed in the measurement error model</em></p> <p><em>literature. We validate our theoretical findings and the effectiveness of the proposed solution</em></p> <p><em>on both synthesized and real datasets.</em></p>