mlsanityData to 7 Oct 2026

Copula-Based Normalizing Flows

arXiv 2107.07352 ↗First posted 15 Jul 2021cs.LG cs.AI stat.MLcited by 5

Not on the map. Why?

Abstract (arXiv)

Normalizing flows, which learn a distribution by transforming the data to samples from a Gaussian base distribution, have proven powerful density approximations. But their expressive power is limited by this choice of the base distribution. We, therefore, propose to generalize the base distribution to a more elaborate copula distribution to capture the properties of the target distribution more accurately. In a first empirical analysis, we demonstrate that this replacement can dramatically improve the vanilla normalizing flows in terms of flexibility, stability, and effectivity for heavy-tailed data. Our results suggest that the improvements are related to an increased local Lipschitz-stability of the learned flow.

Key facts. Cited by 5 papers in the map (data through 7 Oct 2026). Builds on 12 of its 23 references that are in the map. First posted on arXiv 15 Jul 2021.

Builds on

12 of 23 references.

References · 12

  1. 2013Auto-Encoding Variational Bayescited by 3,980
  2. 2016Density estimation using Real NVPcited by 2,029
  3. 2019Normalizing Flows for Probabilistic Modeling and Inferencecited by 1,315
  4. 2014NICE: Non-linear Independent Components Estimationcited by 1,052
  5. 2017Masked Autoregressive Flow for Density Estimationcited by 680
  6. 2018FFJORD: Free-form Continuous Dynamics for Scalable Reversible Generative Modelscited by 584
  7. 2019Residual Flows for Invertible Generative Modelingcited by 256
  8. 2016Range Loss for Deep Face Recognition with Long-tailcited by 111
  9. 2017The Devil is in the Tails: Fine-grained Classification in the Wildcited by 89
  10. 2020Understanding and Mitigating Exploding Inverses in Invertible Neural Networkscited by 71
  11. 2019Copula & Marginal Flows: Disentangling the Marginal from its Jointcited by 17
  12. 2020Robust model training and generalisation with Studentising flowscited by 10

Built on by

Cited by year (2026 to 7 Oct)

Citing papers per year: 2022: 3; 2023: 1; 2024: 0; 2025: 0; 2026: 1.

5 papers.

  1. 2022Marginal Tail-Adaptive Normalizing Flowscited by 12
  2. 2022COMET Flows: Towards Generative Modeling of Multivariate Extremes and Tail Dependencecited by 8
  3. 2022Inference and Sampling for Archimax Copulascited by 5
  4. 2023Tensorizing flows: a tool for variational inferencecited by 1
  5. 2026Dynamic Vine Copulas: Detecting and Quantifying Time-Varying Higher-Order Interactionscited by 0