Learning to generate data by estimating gradients of the data distribution
- Generating realistic data with complex patterns, such as images, audio, or molecular structures, often relies on expressive probabilistic models to represent and estimate high- dimensional data distributions. However, even with the power of deep neural networks, building powerful probabilistic models is non-trivial. One major challenge is the need to normalize probability distributions; that is, to ensure the total probability equals one. This necessitates summing over all possible model outputs, which quickly becomes impractical in high-dimensional spaces. In this dissertation, I propose to address this difficulty by working with data distributions through their score functions. These functions, defined as gradients of log data densities, capture information about the corresponding data distributions without requiring normalization, hence can be modeled with highly flexible deep neural networks. This dissertation is organized into three parts. In Part I, I show how to estimate the score function from a finite dataset with expressive deep neural networks and efficient statistical methods. In Part II, I discuss several ways to generate new data samples from models of score functions, building upon ideas from homotopy methods, Markov chain Monte Carlo, diffusion processes, and differential equations. The resulting score-based generative models (also known as diffusion models) achieved record-breaking generation performance for numerous data modalities, challenging the long-standing dominance of generative adversarial networks on many tasks. Importantly, the sampling procedure of score-based generative models can be flexibly controlled for solving inverse problems, demonstrated by their superior performance on multiple tasks in medical image reconstruction. In Part III, I show how to evaluate probability values accurately with models of score functions. Taken together, score-based generative models provide a flexible, powerful and versatile solution for data generation in machine learning and many other disciplines of science and engineering.
|Type of resource
|electronic resource; remote; computer; online resource
|1 online resource.
|Song, Yang, (Researcher on data distribution)
|Degree committee member
|Degree committee member
|Stanford University, Computer Science Department
|Statement of responsibility
|Submitted to the Computer Science Department.
|Thesis Ph.D. Stanford University 2022.
- © 2022 by Yang Song
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