mlsanityData to 14 Oct 2026

Causal Modeling with Stationary Diffusions

arXiv 2310.17405 ↗First posted 26 Oct 2023cs.LGcited by 19

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Abstract (arXiv)

We develop a novel approach towards causal inference. Rather than structural equations over a causal graph, we learn stochastic differential equations (SDEs) whose stationary densities model a system's behavior under interventions. These stationary diffusion models do not require the formalism of causal graphs, let alone the common assumption of acyclicity. We show that in several cases, they generalize to unseen interventions on their variables, often better than classical approaches. Our inference method is based on a new theoretical result that expresses a stationarity condition on the diffusion's generator in a reproducing kernel Hilbert space. The resulting kernel deviation from stationarity (KDS) is an objective function of independent interest.

Key facts. Cited by 19 papers in the map (data through 14 Oct 2026). Builds on 29 of its 90 references that are in the map. First posted on arXiv 26 Oct 2023.

Builds on

29 of 90 references.

References · 29

  1. 2018DAGs with NO TEARS: Continuous Optimization for Structure Learningcited by 752
  2. 2017Learning Generative Models with Sinkhorn Divergencescited by 314
  3. 2019Causality for Machine Learningcited by 243
  4. 2016A Kernelized Stein Discrepancy for Goodness-of-fit Tests and Model Evaluationcited by 236
  5. 2020Differentiable Causal Discovery from Interventional Datacited by 218
  6. 2020DYNOTEARS: Structure Learning from Time-Series Datacited by 200
  7. 2018Gaussian Processes and Kernel Methods: A Review on Connections and Equivalencescited by 192
  8. 2016Foundations of Structural Causal Models with Cycles and Latent Variablescited by 134
  9. 2017Causal Consistency of Structural Equation Modelscited by 118
  10. 2020Learning Stable Deep Dynamics Modelscited by 111
  11. 2022Optimal Transport Tools (OTT): A JAX Toolbox for all things Wassersteincited by 101
  12. 2015Measuring Sample Quality with Stein's Methodcited by 94
17 more
  1. 2021Proximal Optimal Transport Modeling of Population Dynamicscited by 93
  2. 2018The Lyapunov Neural Network: Adaptive Stability Certification for Safe Learning of Dynamical Systemscited by 88
  3. 2017Permutation-based Causal Inference Algorithms with Interventionscited by 78
  4. 2013Learning Gaussian Networkscited by 62
  5. 2022On the Identifiability and Estimation of Causal Location-Scale Noise Modelscited by 56
  6. 2021Neural graphical modelling in continuous-time: consistency guarantees and algorithmscited by 42
  7. 2014From Ordinary Differential Equations to Structural Causal Models: the deterministic casecited by 41
  8. 2015backShift: Learning causal cyclic graphs from unknown shift interventionscited by 37
  9. 2020Causal models for dynamical systemscited by 34
  10. 2022Active Learning for Optimal Intervention Design in Causal Modelscited by 31
  11. 2018Causal Modeling of Dynamical Systemscited by 24
  12. 2023Causal machine learning for single-cell genomicscited by 23
  13. 2013Cyclic Causal Discovery from Continuous Equilibrium Datacited by 21
  14. 2023NODAGS-Flow: Nonlinear Cyclic Causal Structure Learningcited by 20
  15. 2021Matching a Desired Causal State via Shift Interventionscited by 16
  16. 2020Graphical continuous Lyapunov modelscited by 9
  17. 2013A Polynomial-Time Algorithm for Deciding Markov Equivalence of Directed Cyclic Graphical Modelscited by 7

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Cited by year (2026 to 14 Oct)

Citing papers per year: 2024: 4; 2025: 6; 2026: 9.

19 papers.

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  1. 2024Identifying Drift, Diffusion, and Causal Structure from Temporal Snapshotscited by 13
  2. 2024Scalable and Flexible Causal Discovery with an Efficient Test for Adjacencycited by 6
  3. 2025Counterfactual reasoning: an analysis of in-context emergencecited by 4
  4. 2026Towards Continuous-time Causal Foundation Modelscited by 4
  5. 2025No Foundations without Foundations -- Why semi-mechanistic models are essential for regulatory biologycited by 3
  6. 2026Latent Causal Diffusions for Single-Cell Perturbation Modelingcited by 2
  7. 2026Efficient Learning of Stationary Diffusions with Stein-type Discrepanciescited by 2
  8. 2026Causal Representation Meets Stochastic Modeling under Generic Geometrycited by 2
  9. 2024ExDAG: an MIQP Algorithm for Learning DAGscited by 1
  10. 2024Identifying biological perturbation targets through causal differential networkscited by 1
  11. 2025Towards Identifiability of Interventional Stochastic Differential Equationscited by 1
  12. 2025A Generative Framework for Causal Estimation via Importance-Weighted Diffusion Distillationcited by 0
7 more
  1. 2025Learning Joint Interventional Effects from Single-Variable Interventions in Additive Modelscited by 0
  2. 2025Cyclic Counterfactuals under Shift-Scale Interventionscited by 0
  3. 2026Sign Identifiability of Causal Effects in Stationary Stochastic Dynamical Systemscited by 0
  4. 2026Generative Modeling with Flux Matchingcited by 0
  5. 2026Reconciling Causality and Non-Equilibrium Thermodynamics with Hamiltonian Causal Modelscited by 0
  6. 2026Non-parametric recovery of causal diffusion mechanisms from steady-state observationscited by 0
  7. 2026One Intervention per Component is Enough: Towards Identifiability in Linear Stochastic Dynamics from Steady Statecited by 0

Similar, not cited

Close in wording, no citation either way

  1. 2024A Dynamical View of the Question of Why
  2. 2025Foundations of Diffusion Models in General State Spaces: A Self-Contained Introduction
  3. 2023Diffusion Model in Causal Inference with Unmeasured Confounders
  4. 2025Learning Causal States Under Partial Observability and Perturbation
  5. 2024Stability and Generalizability in SDE Diffusion Models with Measure-Preserving Dynamics
  6. 2023Modeling Causal Mechanisms with Diffusion Models for Interventional and Counterfactual Queries
  7. 2022Markov categories, causal theories, and the do-calculus
  8. 2026Beyond Directed Acyclic Graphs: Causal Zeros and Causal Differential Equations