Model-Informed Flows for Bayesian Inference

Justin Domke (University of Massachusetts, Amherst) · Joohwan Ko (University of Massachusetts Amherst)

complex modelsempirical performanceflow-based variational familiesforward autoregressive flowfull-rank gaussianhierarchical bayesian modelshierarchical orderinginput from priormodel-informed flowposterior approximationsposterior geometrystate-of-the-art benchmarks theoretical insighttranslation termvariational inferencevariationally inferred parameters

Variational inference often struggles with the posterior geometry exhibited by complex hierarchical Bayesian models. Recent advances in flow‐based variational families and Variationally Inferred Parameters (VIP) each address aspects of this challenge, but their formal relationship is unexplored. Here, we prove that the combination of VIP and a full-rank Gaussian can be represented exactly as a forward autoregressive flow augmented with a translation term and input from the model’s prior. Guided by this theoretical insight, we introduce the Model‐Informed Flow (MIF) architecture, which adds the necessary translation mechanism, prior information, and hierarchical ordering. Empirically, MIF delivers tighter posterior approximations and matches or exceeds state‐of‐the‐art performance across a suite of hierarchical and non‐hierarchical benchmarks.