Model-embedding flows: Combining the inductive biases of model-free deep learning and explicit probabilistic modeling

Normalizing flows have shown great success as general-purpose density estimators. However, many real-world applications require the use of domain-specific knowledge, which normalizing flows cannot readily incorporate. We propose embedded-model flows (EMF), which alternate general-purpose transformations with structured layers that embed domain-specific inductive biases. These layers are automatically constructed by converting user-specified differentiable probabilistic models into equivalent bijective transformations. We also introduce gated structured layers, which allow bypassing the parts of the models that fail to capture the statistics of the data. We demonstrate that EMFs can be used to induce desirable properties such as multimodality, hierarchical coupling and continuity. Furthermore, we show that EMFs enable a high-performance form of variational inference where the structure of the prior model is embedded in the variational architecture. In our experiments, we show that this approach outperforms state-of-the-art methods in common structured inference problems.