Training normalizing flow generative models can be challenging due to the need to calculate computationally expensive determinants of Jacobians. This paper studies the likelihood-free training of flows and proposes the energy objective, an alternative sample-based loss based on proper scoring rules. The energy objective is determinant-free and supports flexible model architectures that are not easily compatible with maximum likelihood training, including semi-autoregressive energy flows, a novel model family that interpolates between fully autoregressive and non-autoregressive models. Energy flows feature competitive sample quality, posterior inference, and generation speed relative to likelihood-based flows; this performance is decorrelated from the quality of log-likelihood estimates, which are generally very poor. Our findings question the use of maximum likelihood as an objective or a metric, and contribute to a scientific study of its role in generative modeling.

翻译：训练归一化流生成模型因需计算雅可比行列式的高代价而颇具挑战。本文研究了流的无似然训练，并提出了基于适当评分规则的替代样本损失——能量目标。该能量目标无需行列式计算，且支持灵活模型架构（如半自回归能量流），这类新颖模型族可插值于全自回归与非自回归模型之间，难以直接适配最大似然训练。相较于基于似然的流模型，能量流在样本质量、后验推断及生成速度方面具有竞争力；其性能与对数似然估计质量（通常极差）无相关性。本研究发现对最大似然作为目标函数或评估指标的使用提出质疑，并推动了对其在生成建模中作用的科学研究。