When Does Structure Help? Statistical Tradeoffs for Structured Reverse Processes in Diffusion Large Language Models

dLLMs usually denoise by predicting masked tokens independently, but it is unclear when and whether explicit token coupling through data structure can improve their theoretical guarantees and translate into practical gains. In this work, we prove the first learning-error analysis of dLLMs with structured reverse processes based on graphical models, including tree CRFs, bounded-treewidth clique-tree extensions, and Hidden Markov Model probabilistic circuits (HMM-PCs), covering a broad spectrum of text-data structures. Our main result first decouples the dLLM learning error into estimation, optimization, and structural approximation, and then analyzes the role of each term. For the approximation error, a path-sensitive analysis bounds the contribution of an edge missing from the tree by the geometric decay of correlations along its tree-distance detour, yielding a structure-selection criterion that can disagree with Chow--Liu when correlations are weak. We also identify a tradeoff between approximation bias and estimation error, which yields a slowly-increasing preferred width $w^\star{=}\Theta(\log n)$ as a data-to-structure-capacity scaling regime. From the empirical perspective, we first conduct controlled simulation experiments on synthetic and small-text settings (WikiText-103) to validate the predicted finite-sample signatures of our theory, including exponential path decay on chain MRFs, a bound-optimal tree that disagrees with Chow--Liu, and the balance between different error terms. Then, in the real-world setting, across models ranging from $13$M to $1.1$B parameters, we show that the same HMM-PC teacher is helpful in from-scratch training, mildly negative in SFT distillation at pretrained scale, and substantially helpful in inference-time guidance, supporting the conclusion that both the structural prior and the deployment interface are critical, with the prior providing token-coupling structure and the interface determining whether that structure transfers positively or negatively at a given scale.