High-stakes synthetic data generation faces a fundamental Quadrilemma: achieving Fidelity to the original distribution, Control over complex logical constraints, Reliability in uncertainty estimation, and Efficiency in computational cost -- simultaneously. State-of-the-art Deep Generative Models (CTGAN, TabDDPM) excel at fidelity but rely on inefficient rejection sampling for continuous range constraints. Conversely, Structural Causal Models offer logical control but struggle with high-dimensional fidelity and complex noise inversion. We introduce JANUS (Joint Ancestral Network for Uncertainty and Synthesis), a framework that unifies these capabilities using a DAG of Bayesian Decision Trees. Our key innovation is Reverse-Topological Back-filling, an algorithm that propagates constraints backwards through the causal graph, achieving 100% constraint satisfaction on feasible constraint sets without rejection sampling. This is paired with an Analytical Uncertainty Decomposition derived from Dirichlet priors, enabling 128x faster uncertainty estimation than Monte Carlo methods. Across 15 datasets and 523 constrained scenarios, JANUS achieves state-of-the-art fidelity (Detection Score 0.497), eliminates mode collapse on imbalanced data, and provides exact handling of complex inter-column constraints (e.g., Salary_offered >= Salary_requested) where baselines fail entirely.
Figures & tables
Figure 1: JANUS Architecture. Left: Causal DAG where each node is a feature. Right: Each non-root node is modeled by a Bayesian Decision Tree. Leaves store dual information : Dirichlet posteriors α for forward P(Y∣X) and histograms H for backward P(X∣Y) . Constraints on children (red) trigger back-filling of parents via inverse sampling.
Figure 2: Back-filling Algorithm. Phase 1 : Given constraint “Loan=Approved”, we propagate backward to find which Income values can satisfy it (e.g., Inc > $80k). Phase 2 : Sample parents (Age, Edu) normally, then sample Income from the filtered range, guaranteeing the constraint is satisfied without rejection.
Figure 3: Epistemic Uncertainty Validation. Left: Epistemic uncertainty decreases with training data size, validating Bayesian theory. Middle: Epistemic vs. aleatoric decomposition shows distinct uncertainty sources. Right: Model accuracy improves with more training data. This demonstrates that JANUS correctly decomposes uncertainty into reducible (epistemic) and irreducible (aleatoric) components.
Figure 4: Uncertainty Terrain Map. (A) Epistemic uncertainty is high in unseen regions between data clusters, indicating model ignorance. (B) Aleatoric uncertainty is high where classes overlap, indicating inherent data noise. This 2D visualization (PCA projection, 97.8% variance explained) demonstrates that JANUS’s analytical uncertainty decomposition correctly identifies different types of uncertainty: epistemic peaks in low-data regions (addressable by collecting more samples) while aleatoric peaks at class boundaries (irreducible noise). The distinct spatial patterns validate the theoretical decomposition from Equations ( 3 )–( 5 ).
Figure 5: (a) Pareto frontier : JANUS ( J ) achieves best speed-quality tradeoff (top-left is optimal). D=DCM, T=TVAE, C=CTGAN, R=CAREFL. (b) The Computational Wall : Deep learning methods (CTGAN, TVAE, TabDDPM) require rejection sampling for constraints, causing sample counts to grow exponentially as constraints tighten ( y -axis, log scale). JANUS remains flat at y=1 (guaranteed satisfaction without rejection). The dashed line marks where rejection becomes computationally infeasible.
Type
Best
Score
Gap to Oracle
Equality ( = )
JANUS
0.963
2.9%
Inequality ( ≥ )
JANUS
0.927
6.4%
Inter-Column
JANUS
0.930
6.0%
Mixed
JANUS
0.978
1.2%
Table 3: Performance by Constraint Type
Figure 6: Counterfactual Error Scaling by Graph Complexity. (1) Left : NLIN (additive noise)—all methods perform similarly since noise inversion is straightforward. (2) Right : NADD (non-additive noise)—flow-based methods exhibit high error and variance (shaded regions show ±1 standard deviation) due to numerical instability when inverting multiplicative noise. JANUS (green) achieves 18 × lower error on Chain by avoiding inversion via discrete bin lookup.
Figure 7: Counterfactual Error Distribution (NADD Noise). Violin plots showing error distributions across methods. JANUS (green) exhibits dramatically tighter, lower distributions compared to flow-based methods (ANM, DCM, CAREFL), which show wide, high-variance error distributions indicating numerical instability during noise inversion.
Figure 8: MCS Stability Across Trials. Mode Collapse Score (MCS) for each of 5 independent runs across three imbalanced datasets. MCS measures minority class preservation (1.0 = perfect, lower = mode collapse). (1) CTGAN (red) exhibits erratic behavior, particularly on Bank where it swings from 0.95 to 0.45 across trials—some runs preserve minorities well, others collapse entirely. (2) JANUS (blue) maintains consistent performance near the optimal value with minimal variance ( σ=0.006 ). Shaded regions show ±1 standard deviation. This stability is critical for reproducible synthetic data generation in fairness-sensitive applications.
Figure 9: Forbidden Zone Analysis. Scatter plot for Salaryoffered≥Salaryrequested . The diagonal is the constraint boundary; the red region below is “forbidden.” Baselines (grey) violate the constraint; JANUS (blue) adheres perfectly with 0% violations.