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.

翻译：正规化流是直接最大化似然的生成模型。以往，正规化流的设计在很大程度上受限于解析可逆性的需求。我们通过一种训练程序克服了这一限制，该程序使用变量变换公式梯度的有效估计器。这使得任何保持维度的神经网络都能通过最大似然训练作为生成模型。我们的方法允许将重点放在精确地为手头任务定制归纳偏置上。具体而言，我们利用$E(n)$-等变网络在分子生成基准测试中取得了优异的结果。此外，我们的方法在逆向问题基准测试中具有竞争力，同时使用了现成的ResNet架构。