mlsanityData to 14 Oct 2026

Diffusion Model in Causal Inference with Unmeasured Confounders

arXiv 2308.03669 ↗First posted 7 Aug 2023cs.LG cs.AI stat.MLcited by 3

On the map: Diffusion models → Diffusion foundations and sampling

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Abstract (arXiv)

We study how to extend the use of the diffusion model to answer the causal question from the observational data under the existence of unmeasured confounders. In Pearl's framework of using a Directed Acyclic Graph (DAG) to capture the causal intervention, a Diffusion-based Causal Model (DCM) was proposed incorporating the diffusion model to answer the causal questions more accurately, assuming that all of the confounders are observed. However, unmeasured confounders in practice exist, which hinders DCM from being applicable. To alleviate this limitation of DCM, we propose an extended model called Backdoor Criterion based DCM (BDCM), whose idea is rooted in the Backdoor criterion to find the variables in DAG to be included in the decoding process of the diffusion model so that we can extend DCM to the case with unmeasured confounders. Synthetic data experiment demonstrates that our proposed model captures the counterfactual distribution more precisely than DCM under the unmeasured confounders.

Key facts. Cited by 3 papers in the map (data through 14 Oct 2026). Placed in Diffusion foundations and sampling, one of 14 directions in Diffusion models. Builds on 15 of its 24 references that are in the map. First posted on arXiv 7 Aug 2023.

Builds on

15 of 24 references.

Closest ancestors · 5

Same direction, newest first

  1. 2023Modeling Causal Mechanisms with Diffusion Models for Interventional and Counterfactual Queries2 Feb
  2. 2022Diffusion Models for Causal Discovery via Topological Ordering12 Oct
  3. 2022Understanding Diffusion Models: A Unified Perspective25 Aug
  4. 2020Denoising Diffusion Implicit Models6 Oct
  5. 2020Denoising Diffusion Probabilistic Models19 Jun

Other references · 10

  1. 2015Deep Unsupervised Learning using Nonequilibrium Thermodynamicscited by 7,058
  2. 2022Hierarchical Text-Conditional Image Generation with CLIP Latentscited by 6,585
  3. 2022Photorealistic Text-to-Image Diffusion Models with Deep Language Understandingcited by 6,355
  4. 2020DiffWave: A Versatile Diffusion Model for Audio Synthesiscited by 1,354
  5. 2013Causal Discovery with Continuous Additive Noise Modelscited by 255
  6. 2013CAM: Causal additive models, high-dimensional order search and penalized regressioncited by 178
  7. 2022Score matching enables causal discovery of nonlinear additive noise modelscited by 111
  8. 2020Causal Autoregressive Flowscited by 99
  9. 2022Causal Machine Learning for Healthcare and Precision Medicinecited by 68
  10. 2021VACA: Design of Variational Graph Autoencoders for Interventional and Counterfactual Queriescited by 19

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Cited by year

Citing papers per year: 2024: 1; 2025: 2.

3 papers.

  1. 2024A Survey on Diffusion Models for Time Series and Spatio-Temporal Datacited by 67
  2. 2025A Generative Framework for Causal Estimation via Importance-Weighted Diffusion Distillationcited by 0
  3. 2025Partially Functional Dynamic Backdoor Diffusion-based Causal Modelcited by 0

Similar, not cited

Close in wording, no citation either way

  1. 2024DiffusionCounterfactuals: Inferring High-dimensional Counterfactuals with Guidance of Causal Representations
  2. 2025When Additive Noise Meets Unobserved Mediators: Bivariate Denoising Diffusion for Causal Discovery
  3. 2024LLM-initialized Differentiable Causal Discovery
  4. 2024DiffPO: A causal diffusion model for learning distributions of potential outcomes
  5. 2026Causality-Encoded Diffusion Models for Interventional Sampling and Edge Inference
  6. 2023Diffusion Based Causal Representation Learning
  7. 2025dcFCI: Robust Causal Discovery Under Latent Confounding, Unfaithfulness, and Mixed Data
  8. 2024Counterfactual Causal Inference in Natural Language with Large Language Models