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Conditional Generative Models are Sufficient to Sample from Any Causal Effect Estimand
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Proposes ID-GEN, a sound and complete recursive algorithm that follows the ID identification algorithm to train conditional generative (mainly diffusion) models and wire them into a sampling network for high-dimensional interventional sampling under unobserved confounding.
Problem
Sampling from identifiable interventional distributions P(y|do(x)) when variables are high-dimensional (images, text) and unobserved confounders are present, where likelihood-based identification algorithms need conditional probability tables.
Approach
Recursively follow the ID algorithm's steps to decide which conditional generative models to train (via ConditionalGMs, MergeNetwork, Update), connect them into a feed-forward sampling network whose ancestral sampling yields interventional samples; uses classifier-free diffusion guidance as the conditional model, and sampling for conditional queries via IDC-GEN.
Key results
- On Colored MNIST, ID-GEN achieves FID 25.66 and 22.67 for the two interventions, the lowest among compared methods.
- On color-attribute interventional likelihoods, ID-GEN reaches total variation distance 0.25 versus 0.54 for Cond and 0.58 for DCM.
- On CelebA, EGSDE assigns high probability to causal attributes (WearingLipstick 82%) and non-causal ones (Attractive 37.61%, Young 24.76%), while StarGAN introduces new attributes with probability at most 30%.
Measured effects reported in the paper
| What was changed | Where | Measured | Effect |
|---|---|---|---|
| Use ID-GEN instead of Cond | Colored MNIST causal image intervention · Colored MNIST, do(X) | TVD: 0.54 -> 0.25 | Helped |
| Use ID-GEN instead of DCM | Colored MNIST causal image intervention · Colored MNIST, do(X) | TVD: 0.58 -> 0.25 | Helped |
| Account for latent confounders when sampling interventional images | Colored MNIST · Colored MNIST, do(X) | color-distribution bias | Helped |
| Use EGSDE for domain translation | CelebA image translation · CelebA, do(Male=0) | proportion of images with non-causal attributes: Attractive to 37.61%; Young to 24.76% | Hurt |
| Use StarGAN or conditional StarGAN for domain translation | CelebA image translation · CelebA, do(Male=0) | proportion of images with new attributes: ≤ 30% | Hurt |
| Train conditional models to match the identified interventional factors | ID-GEN on MIMIC-CXR · MIMIC-CXR, conditional model distributions | TVD: ≈ 0.05 | Helped |
Surprising findings
- Conditional baselines and DCM show color bias toward red, green, blue for red X, indicating confounding not removed.
- NCM (GAN-based) generates blended colors, making attribute likelihood evaluation infeasible.
Limitations
- Assumes access to the fully specified ADMG and semi-Markovian causal model.
- Only hard interventions do(X=x) are considered; soft interventions are future work.
- Changing the causal query may require retraining some models.
Experimental setup
Datasets: Colored MNIST (semi-synthetic napkin graph) CelebA MIMIC-CXR
Benchmarks: Colored MNIST napkin graph interventional sampling CelebA attribute analysis MIMIC-CXR chest X-ray generation
Metrics: FID total variation distance attribute proportions
Baselines: Cond (classifier-free conditional diffusion) DCM NCM StarGAN EGSDE Stable diffusion-based report-to-xray baseline
Builds on: ID algorithm (Shpitser and Pearl) classifier-free diffusion guidance c-component factorization DCM NCM
Closest papers by meaning
- Modular Learning of Deep Causal Generative Models for High-dimensional Causal Inference (ICML 2024 · similarity 0.90)
- Causal Inference with Conditional Front-Door Adjustment and Identifiable Variational Autoencoder (ICLR 2024 · similarity 0.89)
- Learning Linear Causal Representations from General Environments: Identifiability and Intrinsic Ambiguity (NeurIPS 2024 · similarity 0.89)
- Learning Mixtures of Unknown Causal Interventions (NeurIPS 2024 · similarity 0.88)
- Marginal Causal Flows for Validation and Inference (NeurIPS 2024 · similarity 0.88)
- Differentiable Causal Discovery for Latent Hierarchical Causal Models (ICLR 2025 · similarity 0.88)
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