Normalizing Flows are generative models that directly maximize the
likelihood. Previously, the design of normalizing flows was largely constrained
by the need for analytical invertibility. We overcome this constraint by a
training procedure that uses an efficient estimator for the gradient of the
change of variables formula. This enables any dimension-preserving neural
network to serve as a generative model through maximum likelihood training. Our
approach allows placing the emphasis on tailoring inductive biases precisely to
the task at hand. Specifically, we achieve excellent results in molecule
generation benchmarks utilizing $E(n)$-equivariant networks. Moreover, our
method is competitive in an inverse problem benchmark, while employing
off-the-shelf ResNet architectures.

我们通过使用梯度的有效估计器来克服了正规化流设计受到解析可逆性需求的约束，并实现了任意保持维度的神经网络作为最大似然训练的生成模型，在分子生成基准测试中取得了出色的结果，同时采用现成的 ResNet 架构在一个反问题基准测试中具有竞争力。