Masked Diffusion Models (MDMs) have emerged as one of the most promising paradigms for generative modeling over discrete domains. It is known that MDMs effectively train to decode tokens in a random order, and that this ordering has significant performance implications in practice. This observation raises a fundamental question: can we design a training framework that optimizes for a favorable decoding order? We answer this in the affirmative, showing that the continuous-time variational objective of MDMs, when equipped with multivariate noise schedules, can identify and optimize for a decoding order during training. We establish a direct correspondence between decoding order and the multivariate noise schedule and show that this setting breaks invariance of the MDM objective to the noise schedule. Furthermore, we prove that the MDM objective decomposes precisely into a weighted auto-regressive losses over these orders, which establishes them as auto-regressive models with learnable orders.

Background: Heart failure (HF) research is constrained by limited access to large, shareable datasets due to privacy regulations and institutional barriers. Synthetic data generation offers a promising solution to overcome these challenges while preserving patient confidentiality. Methods: We generated synthetic HF datasets from institutional data comprising 12,552 unique patients using five deep learning models: tabular variational autoencoder (TVAE), normalizing flow, ADSGAN, SurvivalGAN, and tabular denoising diffusion probabilistic models (TabDDPM). We comprehensively evaluated synthetic data utility through statistical similarity metrics, survival prediction using machine learning and privacy assessments. Results: SurvivalGAN and TabDDPM demonstrated high fidelity to the original dataset, exhibiting similar variable distributions and survival curves after applying histogram equalization. SurvivalGAN (C-indices: 0.71-0.76) and TVAE (C-indices: 0.73-0.76) achieved the strongest performance in survival prediction evaluation, closely matched real data performance (C-indices: 0.73-0.76). Privacy evaluation confirmed protection against re-identification attacks. Conclusions: Deep learning-based synthetic data generation can produce high-fidelity, privacy-preserving HF datasets suitable for research applications. This publicly available synthetic dataset addresses critical data sharing barriers and provides a valuable resource for advancing HF research and predictive modeling.

We investigate the impact of dataset-specific hyperparameter, feature encoding, and architecture tuning on five recent model families for tabular data generation through an extensive benchmark on 16 datasets. This study addresses the practical need for a unified evaluation of models that fully considers hyperparameter optimization. Additionally, we propose a reduced search space for each model that allows for quick optimization, achieving nearly equivalent performance at a significantly lower cost.Our benchmark demonstrates that, for most models, large-scale dataset-specific tuning substantially improves performance compared to the original configurations. Furthermore, we confirm that diffusion-based models generally outperform other models on tabular data. However, this advantage is not significant when the entire tuning and training process is restricted to the same GPU budget for all models.

Synthetic data generation holds considerable promise, offering avenues to enhance privacy, fairness, and data accessibility. Despite the availability of various methods for generating synthetic tabular data, challenges persist, particularly in specialized applications such as survival analysis. One significant obstacle in survival data generation is censoring, which manifests as not knowing the precise timing of observed (target) events for certain instances. Existing methods face difficulties in accurately reproducing the real distribution of event times for both observed (uncensored) events and censored events, i.e., the generated event-time distributions do not accurately match the underlying distributions of the real data. So motivated, we propose a simple paradigm to produce synthetic survival data by generating covariates conditioned on event times (and censoring indicators), thus allowing one to reuse existing conditional generative models for tabular data without significant computational overhead, and without making assumptions about the (usually unknown) generation mechanism underlying censoring. We evaluate this method via extensive experiments on real-world datasets. Our methodology outperforms multiple competitive baselines at generating survival data, while improving the performance of downstream survival models trained on it and tested on real data.