mlsanityData to 7 Oct 2026

Causal normalizing flows: from theory to practice

arXiv 2306.05415 ↗First posted 8 Jun 2023cs.LG cs.AI stat.MEcited by 49

On the map: LLM reasoning → Causal reasoning in LLMs

Abstract (arXiv)

In this work, we deepen on the use of normalizing flows for causal reasoning. Specifically, we first leverage recent results on non-linear ICA to show that causal models are identifiable from observational data given a causal ordering, and thus can be recovered using autoregressive normalizing flows (NFs). Second, we analyze different design and learning choices for causal normalizing flows to capture the underlying causal data-generating process. Third, we describe how to implement the do-operator in causal NFs, and thus, how to answer interventional and counterfactual questions. Finally, in our experiments, we validate our design and training choices through a comprehensive ablation study; compare causal NFs to other approaches for approximating causal models; and empirically demonstrate that causal NFs can be used to address real-world problems, where the presence of mixed discrete-continuous data and partial knowledge on the causal graph is the norm. The code for this work can be found at https://github.com/psanch21/causal-flows.

Key facts. Cited by 49 papers in the map (data through 7 Oct 2026). Placed in Causal reasoning in LLMs, one of 17 directions in LLM reasoning. Builds on 25 of its 47 references that are in the map. First posted on arXiv 8 Jun 2023.

Builds on

25 of 47 references.

References · 25

  1. 2014Adam: A Method for Stochastic Optimizationcited by 36,960
  2. 2022Flow Matching for Generative Modelingcited by 5,426
  3. 2019Normalizing Flows for Probabilistic Modeling and Inferencecited by 1,315
  4. 2015Fast and Accurate Deep Network Learning by Exponential Linear Units (ELUs)cited by 1,061
  5. 2017Counterfactual Fairnesscited by 802
  6. 2017Masked Autoregressive Flow for Density Estimationcited by 680
  7. 2016Improving Variational Inference with Inverse Autoregressive Flowcited by 636
  8. 2019Neural Spline Flowscited by 590
  9. 2021Self-Supervised Learning with Data Augmentations Provably Isolates Content from Stylecited by 308
  10. 2020Deep Structural Causal Models for Tractable Counterfactual Inferencecited by 210
  11. 2018Path-Specific Counterfactual Fairnesscited by 179
  12. 2017CausalGAN: Learning Causal Implicit Generative Models with Adversarial Trainingcited by 152
13 more
  1. 2020Algorithmic recourse under imperfect causal knowledge: a probabilistic approachcited by 139
  2. 2020Causal Autoregressive Flowscited by 97
  3. 2022Deep End-to-end Causal Inferencecited by 93
  4. 2022Diffusion Causal Models for Counterfactual Estimationcited by 87
  5. 2022Neural Causal Models for Counterfactual Identification and Estimationcited by 54
  6. 2023Counterfactual Identifiability of Bijective Causal Modelscited by 42
  7. 2021Relating Graph Neural Networks to Structural Causal Modelscited by 39
  8. 2022Indeterminacy in Generative Models: Characterization and Strong Identifiabilitycited by 33
  9. 2023Modeling Causal Mechanisms with Diffusion Models for Interventional and Counterfactual Queriescited by 23
  10. 2021VACA: Design of Variational Graph Autoencoders for Interventional and Counterfactual Queriescited by 18
  11. 2022Personalized Public Policy Analysis in Social Sciences using Causal-Graphical Normalizing Flowscited by 16
  12. 2022Backtracking Counterfactualscited by 15
  13. 2023Causal Flow-based Variational Auto-Encoder for Disentangled Causal Representation Learningcited by 4

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Cited by year (2026 to 7 Oct)

Citing papers per year: 2023: 3; 2024: 11; 2025: 21; 2026: 14.

49 papers.

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  1. 2023Deep Backtracking Counterfactuals for Causally Compliant Explanationscited by 8
  2. 2024Learning Structural Causal Models through Deep Generative Models: Methods, Guarantees, and Challengescited by 8
  3. 2024Marginal Causal Flows for Validation and Inferencecited by 8
  4. 2025DeCaFlow: A deconfounding causal generative modelcited by 8
  5. 2024Deep Learning With DAGscited by 7
  6. 2024A Fixed-Point Approach for Causal Generative Modelingcited by 7
  7. 2024Causality for Tabular Data Synthesis: A High-Order Structure Causal Benchmark Frameworkcited by 7
  8. 2025Distinguishing Cause from Effect with Causal Velocity Modelscited by 6
  9. 2025Position: Causal Machine Learning Requires Rigorous Synthetic Experiments for Broader Adoptioncited by 6
  10. 2025DoubleGen: Debiased Generative Modeling of Counterfactualscited by 6
  11. 2025Practical do-Shapley Explanations with Estimand-Agnostic Causal Inferencecited by 6
  12. 2025Counterfactual Identifiability via Dynamic Optimal Transportcited by 5
37 more
  1. 2024Amortized Inference of Causal Models via Conditional Fixed-Point Iterationscited by 4
  2. 2025CausalMan: A physics-based simulator for large-scale causalitycited by 4
  3. 2025Interpretable Neural Causal Models with TRAM-DAGscited by 4
  4. 2024chiSPN: Characteristic Interventional Sum-Product Networks for Causal Inference in Hybrid Domainscited by 3
  5. 2025Causal Discovery via Quantile Partial Effectcited by 3
  6. 2025Spatial Deconfounder: Interference-Aware Deconfounding for Spatial Causal Inferencecited by 3
  7. 2025DoFlow: Flow-based Generative Models for Interventional and Counterfactual Forecasting on Time Seriescited by 3
  8. 2024Out-of-Distribution Adaptation in Offline RL: Counterfactual Reasoning via Causal Normalizing Flowscited by 2
  9. 2024Mutatis Mutandis: Revisiting the Comparator in Discrimination Testingcited by 2
  10. 2025Towards Reasonable Concept Bottleneck Modelscited by 2
  11. 2023Advancing Counterfactual Inference through Nonlinear Quantile Regressioncited by 1
  12. 2023Simulating counterfactualscited by 1
  13. 2024Causal Order Discovery based on Monotonic SCMscited by 1
  14. 2025Privilege Scorescited by 1
  15. 2025Causal Posterior Estimationcited by 1
  16. 2025Flow IV: Counterfactual Inference In Nonseparable Outcome Models Using Instrumental Variablescited by 1
  17. 2025Sensitivity Analysis to Unobserved Confounding with Copula-based Normalizing Flowscited by 1
  18. 2026From Universal to Individualized Actionability: Revisiting Personalization in Algorithmic Recoursecited by 1
  19. 2026Joint Treatment Effect Estimation from Incomplete Healthcare Data: Temporal Causal Normalizing Flows with LLM-driven Evolutionary MNAR Imputationcited by 1
  20. 2026Debiased Counterfactual Generation via Flow Matching from Observationscited by 1
  21. 2026CasualSynth: Generating Structurally Sound Synthetic Datacited by 1
  22. 2024Causally Consistent Normalizing Flowcited by 0
  23. 2025On Measuring Intrinsic Causal Attributions in Deep Neural Networkscited by 0
  24. 2025Addressing Correlated Latent Exogenous Variables in Debiased Recommender Systemscited by 0
  25. 2025What is a good matching of probability measures? A counterfactual lens on transport mapscited by 0
  26. 2025Towards Error-Centric Intelligence II: Energy-Structured Causal Modelscited by 0
  27. 2025Reducing normalizing flow complexity for MCMC preconditioningcited by 0
  28. 2026Kolmogorov-Arnold causal generative modelscited by 0
  29. 2026Counterfactual identifiability beyond global monotonicity: non-monotone triangular structural causal modelscited by 0
  30. 2026Physical Simulators as Do-Operators: Causal Discovery under Latent Confounders for AI-for-Sciencecited by 0
  31. 2026Real vs. Semi-Simulated: Rethinking Evaluation for Treatment Effect Estimationcited by 0
  32. 2026Clinically-Grounded Counterfactual Reasoning for Medical Video Diagnosiscited by 0
  33. 2026Causal Variational Deep Embedding: A Family of Interventional Generators for Confounded Imagescited by 0
  34. 2026Implementing Causal Perception: Competing SCMs and Situated Fairnesscited by 0
  35. 2026CAFE: Counterfactual Prediction via Fast Posterior Estimationcited by 0
  36. 2026Beyond Conditional Independence: Root Cause Analysis with Deep Causal Modelscited by 0
  37. 2026Learning Causal Normalizing Flows from Incomplete Data via Observed-Data Likelihoodcited by 0

Similar, not cited

Close in wording, no citation either way

  1. 2025CausalProfiler: Generating Synthetic Benchmarks for Rigorous and Transparent Evaluation of Causal Machine Learning
  2. 2026RepFlow: Representation Enhanced Flow Matching for Causal Effect Estimation
  3. 2025Causal-Copilot: An Autonomous Causal Analysis Agent
  4. 2023NODAGS-Flow: Nonlinear Cyclic Causal Structure Learning
  5. 2026Symmetries and Causality: Causal Effect Identification Beyond IID Data
  6. 2026CausalSteward: An Agentic Divide-Conquer-Combine Copilot for Causal Discovery
  7. 2023Causal Reasoning in the Presence of Latent Confounders via Neural ADMG Learning
  8. 2022Markov categories, causal theories, and the do-calculus