Usefulness of Quantile-Aware Diffusion Modeling for Highly Imbalanced Tabular Data

Abu Talha; Peng Liu; Souradyuti Paul

cs.LGOct 5, 2026

Usefulness of Quantile-Aware Diffusion Modeling for Highly Imbalanced Tabular Data

Authors: Abu Talha, Peng Liu, Souradyuti Paul

Organizations: Indian Institute of Technology Bhilai, Durg, C.G. 491002, India · Loughborough University, Loughborough, LE11 3TU, United Kingdom

Abstract

Classification problem in the context of highly imbalanced data is a major challenge in many real-world applications (e.g., FinTech, healthcare, etc.). In these cases, the vast majority of instances belong to a single class and a small fraction represent the minority class (often the most critical class). Recently, diffusion models have emerged as powerful approaches to reduce the degree of ``imbalanced-ness'' in the dataset; they work by generating synthetic data by capturing complex data distributions using iterative transformations. However, standard diffusion models are not inherently suited to highly skewed or heavy-tailed data, due to inbuilt quadratic error loss, which lacks the structural sensitivity to capture rare, extreme values, and minority-class nuances. We propose a novel approach, namely, Quantile-TabDDPM, based on a quantile-regularized denoising objective that combines the standard quadratic error loss with a quantile loss term to explicitly capture rare events while preserving the theoretical grounding of the original denoising objective. We extensively evaluated our approach on a real-world credit card transaction dataset characterized by extreme class imbalance. The results demonstrate that the integration of diffusion-based synthetic data generation with a quantile-regularized denoising objective provides a robust and effective framework for fraud detection in highly imbalanced datasets.

Figures & tables

Panel of Figure 1 — Figure 1 : Overview of the proposed Quantile-TabDDPM framework for class-conditional generation. Here, $t$ denotes the diffusion timestep and $y$ represents the class label used for conditional generation following the TabDDPM architecture.

Panel of Figure 2 — Figure 2 : Feature-wise distribution comparison between original training data and augmented data (90:10 data augmentation strategy). The blue curves correspond to the original training data, while the yellow curves represent augmented samples. In the first row, augmentation is generated using Quantile-TabDDPM, whereas in the second row, it is generated using the baseline TabDDPM. Each column represents the same feature, enabling direct visual comparison of distributional fidelity across models.

Hyperparameter	Search Space	Selected
Learning rate	Log-uniform $[10^{-5},\,3\times 10^{-3}]$	0.00014106
Batch size	$\{256,512,1024,4096\}$	512
Diffusion timesteps	$\{100,1000\}$	1000
Training epochs	Fixed (1500)	1500
Number of MLP layers	Integer $[2,8]$ (step = 2)	4
Optimizer	AdamW	AdamW

Table 1 : Hyperparameter search space and optimized values for Quantile-TabDDPM on the ECC dataset.

Panel of Figure 3 — Figure 3 : Performance comparison of tree-based classifiers on the ECC dataset using the 90:10 non-fraud-to-fraud augmentation strategy. The bar charts summarize Precision, Recall, F1-score, ROC-AUC, and MCC for (a) Quantile-TabDDPM and (b) the baseline TabDDPM, evaluated on the held-out test set.

Classifier	Quantile-TabDDPM (Ours)					TabDDPM					SMOTE
Classifier	Prec.	Rec.	F1	AUC	MCC	Prec.	Rec.	F1	AUC	MCC	Prec.	Rec.	F1	AUC	MCC
AdaBoost	0.867	0.829	0.842	0.988	0.848	0.704	0.809	0.770	0.976	0.754	0.577	0.837	0.683	0.918	0.695
RandomForest	0.930	0.851	0.876	0.984	0.889	0.826	0.809	0.814	0.992	0.817	0.932	0.837	0.882	0.918	0.883
EasyEnsemble	0.809	0.809	0.809	0.976	0.808	0.500	0.851	0.690	0.990	0.652	0.055	0.939	0.104	0.956	0.224
CatBoost	0.976	0.851	0.889	0.977	0.911	0.800	0.851	0.833	0.991	0.825	0.891	0.837	0.863	0.918	0.863
XGBoost	0.891	0.872	0.879	0.988	0.882	0.886	0.830	0.848	0.990	0.857	0.911	0.837	0.872	0.918	0.873

Table 2 : Performance comparison of Quantile-TabDDPM, TabDDPM (90:10 non-fraud-to-fraud ratio), and SMOTE.

Classifier	CTGAN					TVAE
Classifier	Prec.	Rec.	F1	AUC	MCC	Prec.	Rec.	F1	AUC	MCC
AdaBoost	0.284	0.891	0.431	0.982	0.503	0.408	0.867	0.556	0.985	0.595
RandomForest	0.816	0.869	0.842	0.982	0.842	0.854	0.891	0.872	0.970	0.872
EasyEnsemble	0.053	0.935	0.096	0.987	0.218	0.078	0.891	0.143	0.979	0.261
CatBoost	0.837	0.891	0.863	0.978	0.863	0.796	0.848	0.821	0.984	0.821
XGBoost	0.600	0.913	0.724	0.979	0.739	0.667	0.869	0.755	0.969	0.761

Table 3 : Performance comparison of CTGAN and TVAE (90:10 non-fraud-to-fraud ratio).

Classifier	Precision	Recall	F1-score	ROC-AUC	MCC
AdaBoost	$0.831\pm 0.040$	$0.817\pm 0.044$	$0.820\pm 0.024$	$\mathbf{0.976\pm 0.016}$	$0.823\pm 0.018$
RandomForest	$\mathbf{0.899\pm 0.053}$	$\mathbf{0.857\pm 0.039}$	$\mathbf{0.870\pm 0.025}$	$\mathbf{0.983\pm 0.009}$	$\mathbf{0.877\pm 0.025}$
EasyEnsemble	$0.656\pm 0.088$	$0.738\pm 0.052$	$0.706\pm 0.050$	$0.968\pm 0.020$	$0.694\pm 0.055$
CatBoost	$\mathbf{0.900\pm 0.048}$	$\mathbf{0.849\pm 0.041}$	$\mathbf{0.864\pm 0.020}$	$0.973\pm 0.016$	$\mathbf{0.873\pm 0.016}$
XGBoost	$\mathbf{0.926\pm 0.037}$	$\mathbf{0.853\pm 0.038}$	$\mathbf{0.875\pm 0.027}$	$\mathbf{0.979\pm 0.011}$	$\mathbf{0.888\pm 0.025}$

Table 4 : Monte Carlo simulation aggregate results across 10 independent runs for Quantile-TabDDPM with a 90:10 non-fraud-to-fraud ratio.

Appendix figures & tables5 assets

Supplementary material from the paper’s appendix.

Appendix

Figure 4 : End-to-end workflow of the proposed Quantile-TabDDPM framework for highly imbalanced classification. Rectangles denote processing steps (e.g., training Quantile-TabDDPM, data augmentation, classification), parallelograms represent input/output datasets (original and synthetic data), and arrows indicate the sequential data flow. The process begins with the original credit card dataset, followed by synthetic data generation using TabDDPM with quantile loss, selective extraction of minority (fraud) samples, augmentation of the training dataset, and finally classification using tree-based models.

Classifier	Precision	Recall	F1-score	ROC-AUC	MCC
AdaBoost	$0.818\pm 0.059$	$0.787\pm 0.054$	$0.796\pm 0.042$	$\mathbf{0.973\pm 0.017}$	$0.801\pm 0.041$
RandomForest	$\mathbf{0.896\pm 0.068}$	$\mathbf{0.838\pm 0.038}$	$\mathbf{0.855\pm 0.032}$	$\mathbf{0.977\pm 0.014}$	$\mathbf{0.866\pm 0.037}$
EasyEnsemble	$0.642\pm 0.086$	$0.728\pm 0.059$	$0.693\pm 0.046$	$0.967\pm 0.019$	$0.681\pm 0.050$
CatBoost	$\mathbf{0.902\pm 0.041}$	$\mathbf{0.825\pm 0.048}$	$\mathbf{0.848\pm 0.033}$	$0.971\pm 0.015$	$\mathbf{0.862\pm 0.029}$
XGBoost	$\mathbf{0.925\pm 0.039}$	$\mathbf{0.830\pm 0.049}$	$\mathbf{0.859\pm 0.038}$	$\mathbf{0.976\pm 0.014}$	$\mathbf{0.876\pm 0.034}$

Appendix

Table 5 : Monte Carlo simulation aggregate results across 30 independent runs for Quantile-TabDDPM with a 90:10 non-fraud-to-fraud ratio.

Panel of Figure 5 — Figure 5 : Density plots of classifier performance over 30 independent Monte Carlo simulations for Quantile-TabDDPM (90:10 non-fraud-to-fraud ratio).

Figure 6 : Distribution comparison of original training data vs augmented data using Quantile-TabDDPM

Figure 7 : Distribution comparison of original training data vs augmented data using TabDDPM (baseline model).

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Credit card fraud detection is fundamentally challenged by extreme class imbalance, where fraudulent transactions are rare yet operationally critical. This imbalance often biases supervised learners toward the legitimate class, leading to high overall accuracy but weaker fraud-class recall and F1-score. This paper introduces Q-SYNTH, a hybrid classical--quantum generative adversarial framework in which a parameterized quantum circuit serves as the generator and a classical neural network serves as the discriminator. Q-SYNTH is designed for minority-class fraud synthesis in tabular data and is evaluated along two dimensions: statistical fidelity to real fraud samples and downstream performance for fraud detection. To this end, generated samples are assessed using distributional similarity measures based on Kolmogorov-Smirnov statistics and Wasserstein distances, real-vs-synthetic detectability measured by AUC-ROC, and downstream classification performance across both quantum and classical classifiers. Under the reported protocol, Q-SYNTH reduces marginal distribution mismatch relative to a classical GAN baseline while maintaining competitive downstream fraud-detection performance. Although SMOTE achieves the strongest feature-wise similarity and the classical GAN attains the highest downstream performance in several settings, Q-SYNTH offers a favorable compromise between distributional fidelity and downstream performance, supporting the feasibility of hybrid quantum augmentation for imbalanced fraud detection.

Abstract

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