GENERATIVE IMAGE-TO-IMAGE REGRESSION BASED ON SCORE MATCHING MODELS

Image-to-image regression is an important computer vision research topic. Previous

research works have been concentrating on task-dependent end-to-end regression models. In

this dissertation, we focus on a generative regression framework based on score matching.

Such generative models are called score-based generative models, which learn the data score

functions by gradually adding noise to data using a diffusion process. Images can be generated

with learned score functions through a time-reversal sampling process.

First, we propose a conditional score matching regression framework which targets the

conditional score functions in regression problems. The framework can perform diverse inferences

about conditional distribution by generating samples. We demonstrate its advantages

with various image-to-image regression applications.

Second, we propose a score-based regression model that applies the diffusion process to

both input and response images simultaneously. The proposed method, called synchronized

diffusion, can help stabilize model parameter learning and increase model robustness. In

addition, we develop an effective prediction algorithm based on the Expectation-Maximization

(EM) algorithm which can improve accuracy and computation speed. We illustrate the efficacy

of our proposed approach on high-resolution image datasets.

The last part of the dissertation focuses on analyzing the score-based generative modeling

framework. We conduct a theoretical analysis of the variance exploding behavior observed in

training score-based generative models with denoising score matching objective functions. We

explain the large variance problem from a nonparametric estimation perspective. Furthermore,

we propose a solution to the general score function estimation problem based on Simulation-

Extrapolation (SIMEX), which was originally developed in the measurement error model

literature. We validate our theoretical findings and the effectiveness of the proposed solution

on both synthesized and real datasets.