mlsanityData to 7 Oct 2026

Invertible Generative Modeling using Linear Rational Splines

arXiv 2001.05168 ↗First posted 15 Jan 2020stat.ML cs.LGcited by 39

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Abstract (arXiv)

Normalizing flows attempt to model an arbitrary probability distribution through a set of invertible mappings. These transformations are required to achieve a tractable Jacobian determinant that can be used in high-dimensional scenarios. The first normalizing flow designs used coupling layer mappings built upon affine transformations. The significant advantage of such models is their easy-to-compute inverse. Nevertheless, making use of affine transformations may limit the expressiveness of such models. Recently, invertible piecewise polynomial functions as a replacement for affine transformations have attracted attention. However, these methods require solving a polynomial equation to calculate their inverse. In this paper, we explore using linear rational splines as a replacement for affine transformations used in coupling layers. Besides having a straightforward inverse, inference and generation have similar cost and architecture in this method. Moreover, simulation results demonstrate the competitiveness of this approach's performance compared to existing methods.

Key facts. Cited by 39 papers in the map (data through 7 Oct 2026). First posted on arXiv 15 Jan 2020.

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Citing papers per year: 2021: 8; 2022: 5; 2023: 14; 2024: 7; 2025: 2; 2026: 3.

39 papers.

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  1. 2021Learning Temporally Causal Latent Processes from General Temporal Datacited by 96
  2. 2021Learning Disentangled Representations in the Imaging Domaincited by 46
  3. 2023Counterfactual Identifiability of Bijective Causal Modelscited by 42
  4. 2022Rhino: Deep Causal Temporal Relationship Learning With History-dependent Noisecited by 30
  5. 2023HuManiFlow: Ancestor-Conditioned Normalising Flows on SO(3) Manifolds for Human Pose and Shape Distribution Estimationcited by 23
  6. 2021A Structural Causal Model for MR Images of Multiple Sclerosiscited by 21
  7. 2022Normalizing Flows for Interventional Density Estimationcited by 21
  8. 2023Adversarial robustness of amortized Bayesian inferencecited by 17
  9. 2023A Neural Framework for Generalized Causal Sensitivity Analysiscited by 17
  10. 2021Autoregressive Quantile Flows for Predictive Uncertainty Estimationcited by 15
  11. 2023Reliable Off-Policy Learning for Dosage Combinationscited by 15
  12. 2021Harmonization with Flow-based Causal Inferencecited by 14
27 more
  1. 2024Counterfactual Generation with Identifiability Guaranteescited by 13
  2. 2023A Review of Change of Variable Formulas for Generative Modelingcited by 12
  3. 2022Deep Structural Causal Shape Modelscited by 11
  4. 2022Semi-Autoregressive Energy Flows: Exploring Likelihood-Free Training of Normalizing Flowscited by 9
  5. 2022On the Robustness of Normalizing Flows for Inverse Problems in Imagingcited by 8
  6. 2023Deep Generative Models, Synthetic Tabular Data, and Differential Privacy: An Overview and Synthesiscited by 7
  7. 2024Transformer Neural Autoregressive Flowscited by 7
  8. 2024Preconditioned Neural Posterior Estimation for Likelihood-free Inferencecited by 6
  9. 2021Bootstrap Your Flowcited by 5
  10. 2023One-Line-of-Code Data Mollification Improves Optimization of Likelihood-based Generative Modelscited by 4
  11. 2024One flow to correct them all: improving simulations in high-energy physics with a single normalising flow and a switchcited by 4
  12. 2023Efficient Multimodal Sampling via Tempered Distribution Flowcited by 3
  13. 2023Neural Diffeomorphic Non-uniform B-spline Flowscited by 2
  14. 2021Estimation of Bivariate Structural Causal Models by Variational Gaussian Process Regression Under Likelihoods Parametrised by Normalising Flowscited by 1
  15. 2023A Novel Application of Conditional Normalizing Flows: Stellar Age Inference with Gyrochronologycited by 1
  16. 2023Variational Elliptical Processescited by 1
  17. 2024Design of Restricted Normalizing Flow towards Arbitrary Stochastic Policy with Computational Efficiencycited by 1
  18. 2024Empirical evaluation of normalizing flows in Markov Chain Monte Carlocited by 1
  19. 2026Analytic Bijections for Smooth and Interpretable Normalizing Flowscited by 1
  20. 2026The Wristband Gaussian Loss: Deterministic, Composable Latents via a Sphere-Interval Decompositioncited by 1
  21. 2021Combining Interventional and Observational Data Using Causal Reductionscited by 0
  22. 2023Estimation of Counterfactual Interventions under Uncertaintiescited by 0
  23. 2023Boosting Summarization with Normalizing Flows and Aggressive Trainingcited by 0
  24. 2024Marginalization Consistent Probabilistic Forecasting of Irregular Time Series via Mixture of Separable flowscited by 0
  25. 2025ExOSITO: Explainable Off-Policy Learning with Side Information for Intensive Care Unit Blood Test Orderscited by 0
  26. 2025Set-based Implicit Likelihood Inference of Galaxy Cluster Masscited by 0
  27. 2026Efficient Temporal Point Processes via Monotone Alternating Splinescited by 0