Structured Flow Autoencoders: Learning Structured Probabilistic Representations with Flow Matching

Flow matching has proven to be a powerful density estimator, yet it often fails to explicitly capture the rich inherent latent structure of complex data. To address this limitation, we introduce Structured Flow Autoencoders (SFA), a family of probabilistic models that augments Continuous Normalizing Flows (CNFs) with graphical models. At the core of SFA is a novel flow matching based objective, which explicitly accounts for latent variables, enabling simultaneous learning of likelihood and posterior. We demonstrate the versatility of SFA across settings, including models with continuous and mixture latent variables, as well as latent dynamical systems. Empirical studies show that SFA outperforms Variational Autoencoders (VAE) and their graphical model extensions, achieving better data fit while simultaneously retaining meaningful latent variables as structured representations.