Maximum likelihood (ML) learning for energy-based models (EBMs) is challenging, partly due to non-convergence of Markov chain Monte Carlo.Several variations of ML learning have been proposed, but existing methods all fail to achieve both post-training image generation and proper density estimation. We propose to introduce diffusion data and learn a joint EBM, called diffusion assisted-EBMs, through persistent training (i.e., using persistent contrastive divergence) with an enhanced sampling algorithm to properly sample from complex, multimodal distributions. We present results from a 2D illustrative experiment and image experiments and demonstrate that, for the first time for image data, persistently trained EBMs can {\it simultaneously} achieve long-run stability, post-training image generation, and superior out-of-distribution detection.

翻译：最大似然（ML）学习对于能量模型（EBM）具有挑战性，部分原因在于马尔可夫链蒙特卡洛方法的不收敛性。尽管已有多种ML学习的变体被提出，但现有方法均无法同时实现训练后图像生成与正确的密度估计。我们提出引入扩散数据并通过持久训练（即使用持久对比散度）学习联合能量模型——称为扩散辅助能量模型，配合增强采样算法以正确采样复杂多模态分布。我们展示了二维示例实验和图像实验结果，表明：对于图像数据，这是首次实现持久训练的EBM能够同时保持长期稳定性、训练后图像生成以及卓越的分布外检测能力。