Learning Energy-Based Models in High-Dimensional Spaces with Multi-scale Denoising Score Matching
This work addresses the slow training problem of EBMs for high-dimensional data synthesis, offering a novel approach that improves sample quality and density estimation.
The paper tackles the challenge of training Energy-Based Models (EBMs) efficiently in high-dimensional spaces by proposing a multi-scale denoising score matching method, achieving data generation performance comparable to GANs and setting a new baseline for EBMs.
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.