Beyond Distribution Matching: Semantics-Consistent Tabular Diffusion with Weak Semantic Priors

Yili Wang; Ruxue Shi; Mengnan Du; Hangting Ye; Yi Chang; Xin Wang

cs.LGSep 13, 2026

Beyond Distribution Matching: Semantics-Consistent Tabular Diffusion with Weak Semantic Priors

Authors: Yili Wang, Ruxue Shi, Mengnan Du, Hangting Ye, Yi Chang, Xin Wang

Organizations: School of Artificial Intelligence, Jilin University, Changchun, China · School of Artificial Intelligence, The Chinese University of Hong Kong, Shenzhen, China

Abstract

Synthetic tabular data can match real data distributions while still violating the semantic constraints that govern valid tabular rows. This reveals a key limitation of existing tabular generators: they mainly optimize distributional fidelity, but do not explicitly model weak semantic priors encoded in tabular schema and textual descriptions. In this paper, we propose \ours, a semantics-consistent tabular diffusion framework for high-fidelity synthetic data generation under weakly specified semantic priors. \ours\ first constructs two types of priors, namely intra-column semantics and inter-column symbolic rules, with LLM-assisted extraction from metadata and validation on the real training split. These priors are then used as generation conditions rather than post-hoc filters. Specifically, \ours\ maps heterogeneous column values, column identities, and semantic priors into a unified semantic space, and performs column-wise forward corruption and prior-conditioned reverse denoising to preserve both marginal distributions and rule-consistent cross-column dependencies. Extensive experiments on six real-world tabular benchmarks show that \ours\ consistently improves distributional fidelity, semantic consistency, and downstream task utility over representative VAE-, GAN-, LLM-, and diffusion-based baselines. Additional analyses further demonstrate the robustness of \ours\ when semantic priors are partially unavailable.

Figures & tables

Figure 1: From Distributional Fidelity to Semantically Valid Tabular Generation.

Data	Metric	CTGAN	CTGAN+	TVAE	P-TA	TabDDPM	TABSYN	TABDIFF	SCTab-Diff
Beijing	Shape	80.59 1.18	89.30 6.15	79.32 1.40	88.07 0.27	64.01 30.05	85.24 0.06	98.35 0.28	98.56 0.20
	Trend	80.38 0.62	77.96 5.60	81.67 1.68	76.44 2.89	58.56 31.97	76.32 0.03	96.26 0.23	97.09 0.05
	SA	24.75 18.48	87.84 6.48	19.92 3.38	39.02 2.52	97.03 26.15	97.58 0.07	98.60 0.30	98.68 0.05
News	Shape	83.86 0.66	49.56 1.74	83.07 0.39	96.13 0.03	13.52 6.21	96.45 0.07	96.62 0.29	96.90 0.30
	Trend	94.82 0.09	89.04 0.43	93.41 0.03	88.49 0.10	28.45 47.59	98.35 0.03	98.14 0.32	98.60 0.20
	SA	0.00 0.00	0.00 0.00	0.00 0.00	0.00 0.00	0.00 0.00	0.76 0.04	1.42 1.17	1.24 0.02

Table 1: Data fidelity evaluation results. Shape(%)

\uparrow

evaluates marginal distribution, while Trend(%)

\uparrow

and SA(%)

\uparrow

evaluate data fidelity.

\uparrow

indicates that higher values are better. The best results are highlighted in bold, and suboptimal results are marked with an underline.

Data	Metrics	Real	Method SCTab-Diff
Data	Metrics	Real	CTGAN	CTGAN+	TVAE	P-TA	TabDDPM	TABSYN	TABDIFF
Beijing	RMSE $\downarrow$	0.421 0.005	0.850 0.054	0.960 0.180	0.833 0.058	1.324 0.131	0.634 1.331	0.613 0.024	0.582 0.012	0.498 0.005
News	RMSE $\downarrow$	0.853 0.005	0.860 0.015	6.840 0.030	0.993 0.045	0.821 0.011	3.104 0.000	0.846 0.019	0.864 0.021	0.817 0.003
Shoppers	AUC $\uparrow$	0.924 0.100	0.880 0.740	0.881 1.412	0.885 2.024	0.913 0.543	0.814 18.364	0.888 0.763	0.923 0.214	0.932 0.201
Adult	AUC $\uparrow$	0.925 0.250	0.892 0.132	0.898 0.073	0.887 1.194	0.916 0.152	0.909 0.380	0.897 0.432	0.912 0.081	0.913 0.072
Default	AUC $\uparrow$	0.765 0.133	0.735 0.744	0.687 7.472	0.726 1.362	0.743 0.170	0.759 0.182	0.750 0.784	0.746 0.392	0.771 0.481

Table 2: MLE scores to evaluate downstream task availability. The best results are highlighted in bold, and suboptimal ones are marked with an underline.

Figure 3: Robustness to incomplete semantic priors on Beijing and Adult.

Key Components				Metrics
USS	ICS	ISR	Cw-FP	AUC	Shape	Trend
$\times$	$\times$	$\times$	$\times$	0.741 0.553	96.84 0.32	93.98 0.49
$\checkmark$	$\times$	$\times$	$\times$	0.752 0.523	97.18 0.35	95.21 0.48
$\checkmark$	$\checkmark$	$\times$	$\times$	0.763 0.483	97.56 0.31	95.94 0.55
$\checkmark$	$\checkmark$	$\checkmark$	$\times$	0.769 0.442	97.79 0.14	97.95 0.22
$\checkmark$	$\checkmark$	$\checkmark$	$\checkmark$	0.771 0.481	98.57 0.20	97.89 0.30

Table 3: Ablation results of key designs in SCTab-Diffon Default.

Figure 4: Visualization of categorical column fidelity on News and Shoppers.

Appendix figures & tables18 assets

Supplementary material from the paper’s appendix.

Appendix

h_{t,i}=h_{0,i}+\sigma_{\rho_{i}}(t)\epsilon_{i}

Appendix

Algorithm 1 Training of SCTab-Diff

h_{T,i}\sim\mathcal{N}(0,\sigma_{\rho_{i}}^{2}(T)I)

Appendix

Algorithm 2 Synthetic Tabular Data Generation of SCTab-Diff

Dataset	# Rows	# Num/Cat	# Train/Validation/Test	# Weak Semantic Priors	Task
Adult	48842	6/9	28943/3618/16281	3/13	Classification
Default	30000	14/11	24000/3000/3000	3/24	Classification
Shoppers	12330	10/8	9864/1233/1233	5/17	Classification
Magic	19019	10/1	15215/1902/1902	5/10	Classification
Beijing	43824	7/5	35058/4383/4383	5/11	Regression
News	39644	46/2	31714/3965/3965	10/47	Regression

Appendix

Table 4: Statistics of datasets. # Num/Cat stands for the number of numerical columns and the number of categorical columns, respectively. # Weak Semantic Priors for the number of Inter-Column Symbolic Rules and Intra-Column Semantics, respectively.

Stage	Input	Prompt Template
Constraint generation	Dataset metadata and column schema.	Given the following dataset metadata and column schema, identify semantic constraints that should be satisfied by valid tabular rows. Please extract both intra-column semantics and inter-column symbolic rules. Intra-column semantics describe valid value ranges, valid categories, non-negativity, ordinal meanings, or semantic types of individual columns. Inter-column symbolic rules describe logical dependencies between two or more columns. Please express each constraint as executable Python-style checking code. Do not introduce constraints that are not supported by the metadata or column definitions.
Natural-language conversion	Validated Python-style constraints and dataset metadata.	Given the dataset metadata and the validated Python-style constraints, convert the constraints into concise natural-language descriptions. Organize the output into three parts: Dataset Constraints, Intra-Column Semantics, and Inter-Column Symbolic Rules. Do not introduce new constraints. Use exact column names and preserve the meaning of the validated checking code.

Appendix

Table 5: Prompt templates used for LLM-based weak semantic prior construction.

Methods	Adult	Default	Shoppers	Magic	Beijing	News	Average	Ranking
CTGAN	78.61 1.85	68.48 0.39	78.42 3.32	83.25 0.91	96.12 1.48	97.00 1.03	83.65	5
CTGAN+	93.35 2.68	87.57 4.35	92.73 2.87	41.74 0.78	89.27 11.23	0.00 0.00	67.45	7
TVAE	96.71 1.67	84.11 1.76	62.29 7.40	82.90 0.92	90.58 5.51	89.40 8.92	84.33	4
TabDDPM	96.07 0.34	97.73 0.43	92.53 1.74	98.20 0.73	98.67 0.94	0.00 0.00	69.66	6
TABSYN	94.34 1.36	98.96 0.10	95.09 0.40	90.93 0.19	91.11 0.41	99.30 0.05	94.95	3
TABDIFF	99.41 0.34	98.38 0.47	99.28 0.49	99.32 0.34	98.59 0.10	92.83 2.25	97.97	2

Appendix

Table 6: Comparison of

\alpha

-Precision scores. Bold Face represents the best score on each dataset and marks the suboptimal ones with an underline.

Methods	Adult	Default	Shoppers	Magic	Beijing	News	Average	Ranking
CTGAN	30.24 1.19	19.77 0.64	32.77 0.84	10.67 1.35	40.17 1.42	26.18 1.02	26.63	6
CTGAN+	29.64 7.37	21.59 11.59	17.23 3.02	0.17 0.02	41.65 1.99	0.00 0.00	18.38	7
TVAE	36.67 1.08	21.49 0.98	23.20 2.65	32.47 0.44	26.26 2.29	27.78 1.17	27.98	5
TabDDPM	48.72 0.75	47.16 0.82	54.13 0.74	47.57 0.93	19.13 0.87	0.00 0.00	36.12	3
TABSYN	33.24 0.33	39.54 0.26	38.66 0.94	17.22 0.08	20.34 0.15	44.47 0.04	32.25	4
TABDIFF	49.37 1.21	50.53 0.82	49.51 1.56	46.85 0.79	58.06 0.13	37.32 45.34	48.67	2

Appendix

Table 7: Comparison of

\beta

-Recall scores. Bold Face represents the best score on each dataset and marks the suboptimal ones with an underline.

Methods	Adult	Default	Shoppers	Magic	Beijing	News
CTGAN	0.644 0.054	0.639 0.025	0.711 0.014	0.681 0.014	0.774 0.078	0.695 0.059
CTGAN+	0.436 0.284	0.660 0.095	0.002 0.001	0.020 0.020	0.697 0.220	0.000 0.000
TVAE	0.703 0.057	0.545 0.034	0.297 0.020	0.821 0.031	0.694 0.058	0.441 0.023
TabDDPM	0.960 0.009	0.981 0.011	0.861 0.006	0.984 0.012	0.350 0.534	0.162 0.227
TABSYN	0.572 0.019	0.715 0.004	0.680 0.007	0.720 0.003	0.671 0.001	0.839 0.006
TABDIFF	0.967 0.012	0.949 0.008	0.959 0.029	0.970 0.007	0.960 0.007	0.925 0.029

Appendix

Table 8: Detection score (C2ST) using logistic regression classifier. Bold Face represents the best score on each dataset and marks the suboptimal ones with an underline.

Figure 5: The impact of Condition Guidance Level Parameters $p_{u}$ on MLE, SA, Shape, and Trend across the Adult, Magic, Beijing, and News datasets.

Metric	$p_{u}=0$	$p_{u}=0.1$	$p_{u}=0.2$	$p_{u}=0.5$	$p_{u}=0.9$
Shape(%) $\uparrow$	99.12	98.82	98.56	98.04	97.31
Trend(%) $\uparrow$	97.43	97.46	97.49	96.72	95.84
SA(%) $\uparrow$	98.20	98.75	98.68	98.21	97.36

Appendix

Table 9: Effect of prior masking probability

p_{u}

on data fidelity and semantic consistency. The main experiments use

p_{u}=0.2

Figure 6: Visualization of real and synthetic samples on the Adult dataset.

Figure 7: Visualization of intra-column distribution fidelity on Shoppers and News.

Figure 8: Visualization of inter-column dependency preservation on Shoppers and News.

Panel of Table 10 — Table 10: Weak Semantic Priors of Adult.

Panel of Table 11 — Table 11: Weak Semantic Priors of Shoppers.

Panel of Table 12 — Table 12: Weak Semantic Priors of Default.

Panel of Table 13 — Table 13: Weak Semantic Priors of Magic.

Panel of Table 14 — Table 14: Weak Semantic Priors of Beijing.

Panel of Table 15 — Table 15: Weak Semantic Priors of News.

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Existing approaches for synthetic tabular data generation are based on either purely generative models or LLMs, both of which struggle with data heterogeneity, logical consistency, rare-event coverage, and robustness in low-data regimes. In this paper, we propose a hierarchical hybrid top-down and bottom-up (H-TDBU) framework that decouples semantic structures from stochastic texture. In the top-down path, structure-driven logical constraints and cross-modal alignment rules are constructed, while in the bottom-up path, lightweight tabular generators are used to learn local statistical patterns from real data. The two paths are consolidated in a unified synthesis engine with an iterative feedback loop. We evaluate the framework on weak multimodal financial benchmarks combining tabular and sentiment-text data. Experimental results show that our H-TDBU approach improves train-synthetic-test-real performance over neural baseline methods while preserving semantic consistency. Our results suggest that hierarchical rule-guided synthesis provides an effective mechanism for combining controllability, semantic coherence, and statistical fidelity in synthetic data generation.

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