mlsanityData to 14 Oct 2026

Model-Informed Flows for Bayesian Inference

arXiv 2505.24243 ↗First posted 30 May 2025cs.LG stat.MLcited by 3

Not on the map. Why?

Abstract (arXiv)

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.

Key facts. Cited by 3 papers in the map (data through 14 Oct 2026). Builds on 22 of its 46 references that are in the map. First posted on arXiv 30 May 2025.

Builds on

22 of 46 references.

References · 22

  1. 2014Adam: A Method for Stochastic Optimizationcited by 37,240
  2. 2015Variational Inference with Normalizing Flowscited by 2,170
  3. 2016Density estimation using Real NVPcited by 2,042
  4. 2018Glow: Generative Flow with Invertible 1x1 Convolutionscited by 1,545
  5. 2016Variational Inference: A Review for Statisticianscited by 1,472
  6. 2017Masked Autoregressive Flow for Density Estimationcited by 684
  7. 2016Improving Variational Inference with Inverse Autoregressive Flowcited by 640
  8. 2015MADE: Masked Autoencoder for Distribution Estimationcited by 307
  9. 2022Flow Annealed Importance Sampling Bootstrapcited by 127
  10. 2021Annealed Flow Transport Monte Carlocited by 90
  11. 2019NeuTra-lizing Bad Geometry in Hamiltonian Monte Carlo Using Neural Transportcited by 74
  12. 2022Continual Repeated Annealed Flow Transport Monte Carlocited by 66
10 more
  1. 2024Beyond ELBOs: A Large-Scale Evaluation of Variational Methods for Samplingcited by 56
  2. 2013Hamiltonian Monte Carlo for Hierarchical Modelscited by 52
  3. 2020Advances in Black-Box VI: Normalizing Flows, Importance Weighting, and Optimizationcited by 37
  4. 2021Monte Carlo Variational Auto-Encoderscited by 36
  5. 2020Automatic structured variational inferencecited by 22
  6. 2022A Unified Perspective on Natural Gradient Variational Inference with Gaussian Mixture Modelscited by 22
  7. 2019Automatic Reparameterisation of Probabilistic Programscited by 18
  8. 2021Automatic variational inference with cascading flowscited by 9
  9. 2024Disentangling impact of capacity, objective, batchsize, estimators, and step-size on flow VIcited by 5
  10. 2021Embedded-model flows: Combining the inductive biases of model-free deep learning and explicit probabilistic modelingcited by 3

Built on by

Cited by year (2026 to 14 Oct)

Citing papers per year: 2026: 3.

3 papers.

  1. 2026Corrected Integrated Laplace Approximation for Bayesian Inference in Latent Gaussian Modelscited by 0
  2. 2026Amortized Factor Inference Networks for Posterior Inferencecited by 0
  3. 2026Mode Collapse Is Cheap to Detect: A Ground-Truth-Free Pre-Flight Check for Neural Samplerscited by 0