Learning Energy-Based Models by Cooperative Diffusion Recovery Likelihood

Training energy-based models (EBMs) with maximum likelihood estimation on high-dimensional data can be both challenging and time-consuming. As a result, there a noticeable gap in sample quality between EBMs and other generative frameworks like GANs and diffusion models. To close this gap, inspired by the recent efforts of learning EBMs by maximimizing diffusion recovery likelihood (DRL), we propose cooperative diffusion recovery likelihood (CDRL), an effective approach to tractably learn and sample from a series of EBMs defined on increasingly noisy versons of a dataset, paired with an initializer model for each EBM. At each noise level, the initializer model learns to amortize the sampling process of the EBM, and the two models are jointly estimated within a cooperative training framework. Samples from the initializer serve as starting points that are refined by a few sampling steps from the EBM. With the refined samples, the EBM is optimized by maximizing recovery likelihood, while the initializer is optimized by learning from the difference between the refined samples and the initial samples. We develop a new noise schedule and a variance reduction technique to further improve the sample quality. Combining these advances, we significantly boost the FID scores compared to existing EBM methods on CIFAR-10 and ImageNet 32x32, with a 2x speedup over DRL. In addition, we extend our method to compositional generation and image inpainting tasks, and showcase the compatibility of CDRL with classifier-free guidance for conditional generation, achieving similar trade-offs between sample quality and sample diversity as in diffusion models.