Energy based models (EBMs) are appealing for their generality and simplicity in data likelihood modeling, but have conventionally been difficult to train due to the unstable and time-consuming implicit MCMC sampling during contrastive divergence training. In this paper, we present a novel energy-based generative framework, Variational Potential Flow (VAPO), that entirely dispenses with implicit MCMC sampling and does not rely on complementary latent models or cooperative training. The VAPO framework aims to learn a potential energy function whose gradient (flow) guides the prior samples, so that their density evolution closely follows an approximate data likelihood homotopy. An energy loss function is then formulated to minimize the Kullback-Leibler divergence between density evolution of the flow-driven prior and the data likelihood homotopy. Images can be generated after training the potential energy, by initializing the samples from Gaussian prior and solving the ODE governing the potential flow on a fixed time interval using generic ODE solvers. Experiment results show that the proposed VAPO framework is capable of generating realistic images on various image datasets. In particular, our proposed framework achieves competitive FID scores for unconditional image generation on the CIFAR-10 and CelebA datasets.

翻译：基于能量的模型（EBMs）因其在数据似然建模中的普适性和简洁性而备受关注，但由于对比散度训练过程中隐含的MCMC采样不稳定且耗时，传统上难以训练。本文提出了一种新的基于能量的生成框架——变分势流（VAPO），该框架完全摒弃了隐含的MCMC采样，且不依赖辅助的隐变量模型或协同训练。VAPO框架旨在学习一个势能函数，其梯度（流）引导先验样本，使得其密度演化紧密跟随一个近似的数据似然同伦。随后，通过构建一个能量损失函数来最小化流驱动先验的密度演化与数据似然同伦之间的Kullback-Leibler散度。训练完成后，通过从高斯先验初始化样本，并使用通用ODE求解器在固定时间区间上求解控制势流的常微分方程，即可生成图像。实验结果表明，所提出的VAPO框架能够在多种图像数据集上生成逼真的图像。特别地，我们的框架在CIFAR-10和CelebA数据集上的无条件图像生成任务中取得了具有竞争力的FID分数。