This paper builds bridges between two families of probabilistic algorithms:
(hierarchical) variational inference (VI), which is typically used to model
distributions over continuous spaces, and generative flow networks (GFlowNets),
which have been used for distributions over discrete structures such as graphs.
We demonstrate that, in certain cases, VI algorithms are equivalent to special
cases of GFlowNets in the sense of equality of expected gradients of their
learning objectives. We then point out the differences between the two families
and show how these differences emerge experimentally. Notably, GFlowNets, which
borrow ideas from reinforcement learning, are more amenable than VI to
off-policy training without the cost of high gradient variance induced by
importance sampling. We argue that this property of GFlowNets can provide
advantages for capturing diversity in multimodal target distributions.

这篇文章研究了两​​种概率算法（层次）变分推断（VI）和生成流网络（GFlowNets）之间的关系。作者发现，在某些情况下，VI 算法等价于 GFlowNets 的特殊情况，但 GFlowNets 比 VI 更适宜于强化学习和多模态目标分布的捕捉。

GFlowNets 和变分推断

GFlowNets and variational inference

Based on a new coupling approach, we prove that the transition step of the
Hamiltonian Monte Carlo algorithm is contractive w.r.t. a carefully designed
Kantorovich (L1 Wasserstein) distance. The lower bound for the contraction rate
is explicit. Global convexity of the potential is not required, and thus
multimodal target distributions are included. Explicit quantitative bounds for
the number of steps required to approximate the stationary distribution up to a
given error are a direct consequence of contractivity. These bounds show that
HMC can overcome diffusive behaviour if the duration of the Hamiltonian
dynamics is adjusted appropriately.

通过一种新的耦合方法，我们证明了 Hamiltonian Monte Carlo 算法的转换步对于经过精心设计的 Kantorovich（L1Wasserstein）距离是收缩的。 收敛速率的下界是明确的，全局凸性不是必需的，因此包括多模式目标分布。 收缩性的显式量化界限直接推出了近似到给定误差的稳态分布所需的步骤数。这些界限表明，如果调整 Hamiltonian 动力学的持续时间，则 HMC 可以克服扩散行为。

Hamiltonian Monte Carlo 的耦合与收敛

Coupling and Convergence for Hamiltonian Monte Carlo

Normalizing flows and autoregressive models have been successfully combined
to produce state-of-the-art results in density estimation, via Masked
Autoregressive Flows (MAF), and to accelerate state-of-the-art WaveNet-based
speech synthesis to 20x faster than real-time, via Inverse Autoregressive Flows
(IAF). We unify and generalize these approaches, replacing the (conditionally)
affine univariate transformations of MAF/IAF with a more general class of
invertible univariate transformations expressed as monotonic neural networks.
We demonstrate that the proposed neural autoregressive flows (NAF) are
universal approximators for continuous probability distributions, and their
greater expressivity allows them to better capture multimodal target
distributions. Experimentally, NAF yields state-of-the-art performance on a
suite of density estimation tasks and outperforms IAF in variational
autoencoders trained on binarized MNIST.

本篇研究提出了使用单调神经网络替代对条件仿射单变量转换的方法进行流式变换，称之为神经自回归流（NAF）。实验结果显示，NAF 在密度估计任务上表现出色，并在 MNIST 二值化数据集上的变分自编码器训练中表现出优于 IAF 的性能。