Why LLMs Are Bad at Synthetic Table Generation (and what to do about it)

Synthetic data generation is integral to ML pipelines, e.g., to augment training data, replace sensitive information, and even to power advanced platforms like DeepSeek. While LLMs fine-tuned for synthetic data generation are gaining traction, synthetic table generation -- a critical data type in business and science -- remains under-explored compared to text and image synthesis. This paper shows that LLMs, whether used as-is or after traditional fine-tuning, are inadequate for generating synthetic tables. Their autoregressive nature, combined with random order permutation during fine-tuning, hampers the modeling of functional dependencies and prevents capturing conditional mixtures of distributions essential for real-world constraints. We demonstrate that making LLMs permutation-aware can mitigate these issues.