Research map / Probabilistic and scientific modeling / Causal discovery
Causally Consistent Normalizing Flow
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Proposes CCNF, a causally consistent normalizing flow that uses a topological-batching sequential representation of SCMs and partial causal transformations to stay causally consistent while allowing multiple hidden layers.
Problem
Generative models such as normalizing flows often learn causal graphs that differ from the SCM they should match (causal inconsistency), which can cause issues like unfairness; prior causally consistent models (Causal NF, VACA) restrict depth and lose expressiveness.
Approach
Translate the SCM DAG into an ordered sequence of topological batches and chain partial causal transformations, each updating only one batch's variables conditioned on their parents, so the flow is causally consistent by design with arbitrary depth per batch.
Key results
- CCNF attains zero causal-consistency loss and KL 0.00 on the four-node chain, while CausalNF and VACA are consistent only with a single layer (L=1).
- On intervention/counterfactual tasks CCNF has the lowest KL in 6 of 6 datasets reported, e.g. KL 0.12 vs 0.37 for CausalNF on Nlin-Triangle.
- On German credit, CCNF reaches 75.80% accuracy and 0.00% unfairness, versus SVM 73.00% accuracy and 9.00% unfairness.
Measured effects reported in the paper
| What was changed | Where | Measured | Effect |
|---|---|---|---|
| Use CCNF instead of CausalNF | Causal inference models · Nlin-Triangle | KL: 0.37±0.00 -> 0.12±0.04 | Helped |
| Use CCNF instead of CausalNF | Causal inference models · Nlin-Triangle | Intervention MMD: 0.10±0.02 -> 0.03±0.03 | Helped |
| Use CCNF instead of CausalNF | Causal inference models · Nlin-Triangle | Counterfactual RMSD: 0.79±0.07 -> 0.14±0.05 | Helped |
| Use CCNF instead of CausalNF | Causal inference models · Nlin-Simpson | KL: 0.25±0.00 -> 0.01±0.00 | Helped |
| Use CCNF instead of CausalNF | Causal inference models · Nlin-Simpson | Intervention MMD: 0.04±0.01 -> 0.00±0.00 | Helped |
| Use CCNF instead of CausalNF | Causal inference models · Nlin-Simpson | Counterfactual RMSD: 0.00±0.00 -> 0.00±0.00 | No clear effect |
| Use CCNF instead of the strongest baseline | Causal inference models · M-Graph | KL: 0.32±0.00 -> 0.01±0.00 | Helped |
| Use CCNF instead of the strongest baseline | Causal inference models · M-Graph | Intervention MMD: 0.12±0.01 -> 0.00±0.00 | Helped |
| Use CausalNF instead of CCNF | Causal inference models · M-Graph | Counterfactual RMSD: 0.02±0.01 -> 0.04±0.01 | Hurt |
| Use CCNF instead of CausalNF | Causal inference models · Network | KL: 1.38±0.04 -> 0.55±0.13 | Helped |
| Use CCNF instead of CausalNF | Causal inference models · Network | Intervention MMD: 0.15±0.02 -> 0.01±0.01 | Helped |
| Use CCNF instead of CausalNF | Causal inference models · Network | Counterfactual RMSD: 0.41±0.03 -> 0.25±0.06 | Helped |
Surprising findings
- CausalNF is roughly 2x faster in training and evaluation than CCNF, which the authors describe as about 130% extra time for CCNF.
Limitations
- Requires a well-defined DAG causal graph, which is hard to obtain in practice.
- Cannot handle incorrect or non-DAG causal graphs in its current form.
Experimental setup
Datasets: Nonlinear Triangle Nonlinear Simpson M-Graph Network Backdoor Chain Four Node Chain German credit
Benchmarks: Nonlinear Triangle Nonlinear Simpson M-Graph Network Backdoor Chain German credit
Metrics: KL divergence MMD RMSD causal consistency loss L(T_theta(X)) accuracy F1 individual fairness training and evaluation time
Baselines: CAREFL CausalNF VACA SVM
Builds on: Causal NF CAREFL VACA MAF flow++
Closest papers by meaning
- Learning Structural Causal Models from Ordering: Identifiable Flow Models (AAAI 2025 · similarity 0.88)
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- Causal Inference with Conditional Front-Door Adjustment and Identifiable Variational Autoencoder (ICLR 2024 · similarity 0.86)
- Causality can systematically address the monsters under the bench(marks) (NeurIPS 2026 · similarity 0.86)
- Marginal Causal Flows for Validation and Inference (NeurIPS 2024 · similarity 0.86)
- How to build a consistency model: Learning flow maps via self-distillation (NeurIPS 2025 · similarity 0.85)
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