Maximum likelihood estimation is widely used in training Energy-based models
(EBMs). Training requires samples from an unnormalized distribution, which is
usually intractable, and in practice, these are obtained by MCMC algorithms
such as Langevin dynamics. However, since MCMC in high-dimensional space
converges extremely slowly, the current understanding of maximum likelihood
training, which assumes approximate samples from the model can be drawn, is
problematic. In this paper, we try to understand this training procedure by
replacing Langevin dynamics with deterministic solutions of the associated
gradient descent ODE. Doing so allows us to study the density induced by the
dynamics (if the dynamics are invertible), and connect with GANs by treating
the dynamics as generator models, the initial values as latent variables and
the loss as optimizing a critic defined by the very same energy that determines
the generator through its gradient. Hence the term - self-adversarial loss. We
show that reintroducing the noise in the dynamics does not lead to a
qualitative change in the behavior, and merely reduces the quality of the
generator. We thus show that EBM training is effectively a self-adversarial
procedure rather than maximum likelihood estimation.

本文研究了训练基于能量的模型（EBMs）的最大似然估计方法，通过确定性梯度下降 ODE 解法替换 Langevin 动力学以了解该训练过程，并将动力学视为生成器模型并通过优化由能量确定生成器的梯度定义的评论家来连接 GAN，因此提出了自对抗损失。研究表明，EBM 训练实际上是一种自对抗性的过程，而不是最大似然估计。