Imbalance-Robust and Sampling-Efficient Continuous Conditional GANs via Adaptive Vicinal Learning and Auxiliary Regularization

Conditional diffusion models have become a powerful and flexible framework for learning complex conditional distributions from labeled data. In practice, however, acquiring high-quality labels is costly and time-consuming, leaving large volumes of unlabeled data unused. To address this, we introduce label-augmented conditional diffusion (LACD), a simple and effective approach that incorporates unlabeled examples by assigning them a designated trivial label and performing joint denoising score matching over the augmented dataset. We provide sufficient conditions guaranteeing population-level identifiability of the target conditional distribution under this scheme. Moreover, we establish rigorous statistical guarantees: when sufficiently many unlabeled samples are available, the sampling distribution produced by LACD converges strictly faster than the purely supervised estimator in total variation distance, and at least as fast in Wasserstein-1 distance. Extensive experiments on synthetic, image, and tabular benchmarks corroborate our theory and show substantial gains in sample efficiency and generative performance compared with the purely supervised estimator.

The tabular form constitutes the standard way of representing data in relational database systems and spreadsheets. But, similarly to other forms, tabular data suffers from class imbalance, a problem that causes serious performance degradation in a wide variety of machine learning tasks. One of the most effective solutions dictates the usage of Generative Adversarial Networks (GANs) in order to synthesize artificial data instances for the under-represented classes. Despite their good performance, most of the proposed GAN models do not take into account the vector subspaces of the input samples in the real data space, leading to data generation in arbitrary locations. In addition, the class labels are handled in the same manner as the other categorical variables, so conditional sampling by class is rendered less effective. To overcome these problems, this study presents ctdGAN, a conditional GAN for alleviating class imbalance in tabular datasets. Initially, ctdGAN executes a space partitioning step to assign cluster labels to the input samples. Subsequently, it utilizes these labels to synthesize samples via a novel probabilistic sampling strategy and a new loss function that penalizes both cluster and class mis-predictions. In this way, ctdGAN generates samples in subspaces that resemble those of the original data distribution. We also introduce several other improvements, including a simple, yet effective cluster-wise scaling technique that captures multiple feature modes without affecting data dimensionality. The evaluation of ctdGAN with 14 imbalanced datasets demonstrated its strong ability in generating high fidelity samples and improving classification accuracy.

Generative data augmentation is widely used to mitigate class imbalance, yet its theoretical effect on downstream generalization remains poorly understood. In this work, we develop a statistical framework for conditional generative augmentation and analyze its impact on classification risk. We formalize augmentation as a distribution-mixing process and show that the resulting risk distortion is controlled by both the augmentation strength and the class-conditional Wasserstein discrepancy between real and generated distributions. We further derive a capacity-dependent generalization bound based on Rademacher complexity, revealing an explicit trade-off between hypothesis complexity, augmentation intensity, and generative fidelity. Empirically, we evaluate the framework on binary and multiclass imbalanced classification tasks using Conditional GAN and Conditional WGAN-GP augmentation. Across datasets, CWGAN-GP consistently achieves lower Wasserstein discrepancies than CGAN, indicating improved distributional fidelity. However, improved fidelity does not necessarily translate into superior classification performance, with classical oversampling methods often remaining competitive. These findings support the central theoretical prediction that augmentation reliability is governed by distributional approximation error rather than predictive performance alone. Overall, this work establishes generative augmentation as a distributional perturbation process whose reliability can be quantified through Wasserstein-based measures and supported by finite-sample generalization guarantees. The proposed framework provides a principled foundation for evaluating synthetic data quality beyond classification accuracy alone.