Learning Energy-Based Models in High-Dimensional Spaces with Multi-scale Denoising Score Matching

TL;DR

This paper introduces a novel energy-based model trained with multi-scale denoising score matching, enabling high-quality sample synthesis and data denoising in high-dimensional spaces, outperforming previous EBM methods.

Contribution

The paper proposes a new EBM training method using multi-scale denoising score matching, improving high-dimensional data generation and density estimation.

Findings

Model achieves sample quality comparable to GANs.

Training with multiple noise levels is essential in high dimensions.

Model performs well in image inpainting tasks.

Abstract

Energy-Based Models (EBMs) assign unnormalized log-probability to data samples. This functionality has a variety of applications, such as sample synthesis, data denoising, sample restoration, outlier detection, Bayesian reasoning, and many more. But training of EBMs using standard maximum likelihood is extremely slow because it requires sampling from the model distribution. Score matching potentially alleviates this problem. In particular, denoising score matching \citep{vincent2011connection} has been successfully used to train EBMs. Using noisy data samples with one fixed noise level, these models learn fast and yield good results in data denoising \citep{saremi2019neural}. However, demonstrations of such models in high quality sample synthesis of high dimensional data were lacking. Recently, \citet{song2019generative} have shown that a generative model trained by denoising score matching accomplishes excellent sample synthesis, when trained with data samples corrupted with multiple levels of noise. Here we provide analysis and empirical evidence showing that training with multiple noise levels is necessary when the data dimension is high. Leveraging this insight, we propose a novel EBM trained with multi-scale denoising score matching. Our model exhibits data generation performance comparable to state-of-the-art techniques such as GANs, and sets a new baseline for EBMs. The proposed model also provides density information and performs well in an image inpainting task.