In differentially private (DP) tabular data synthesis, the consensus is that statistical models are better than neural network (NN)-based methods. However, we argue that this conclusion is incomplete and overlooks the challenge of densely correlated datasets, where intricate dependencies can overwhelm statistical models. In such complex scenarios, neural networks are more suitable due to their capacity to fit complex distributions by learning directly from samples. Despite this potential, existing NN-based algorithms still suffer from significant limitations. We therefore propose MargNet, incorporating successful algorithmic designs of statistical models into neural networks. MargNet applies an adaptive marginal selection strategy and trains the neural networks to generate data that conforms to the selected marginals. On sparsely correlated datasets, our approach achieves utility close to the best statistical method while offering an average 7$\times$ speedup over it. More importantly, on densely correlated datasets, MargNet establishes a new state-of-the-art, reducing fidelity error by up to 26\% compared to the previous best. We release our code on GitHub.\footnote{https://github.com/KaiChen9909/margnet}

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