Theoretical Benefit and Limitation of Diffusion Language Model
Guhao Feng, Yihan Geng, Jian Guan, Wei Wu, Liwei Wang, Di He
Diffusion language models have emerged as a new approach for text generation. By enabling the parallel sampling of multiple tokens in each diffusion step, they appear to offer a more efficient alternative to auto-regressive models. However, our observations show that current open-sourced diffusion language models require more sampling steps to achieve comparable accuracy on representative tasks--resulting in even higher inference costs than their auto-regressive counterparts. To investigate whether this is an inherent limitation, we conduct a rigorous theoretical analysis of a widely adopted variant: the Masked Diffusion Model (MDM). Surprisingly, our analysis reveals that the conclusion is highly sensitive to the choice of evaluation metric. Under mild conditions, we prove that when the target is near-optimal perplexity, MDMs can achieve this goal in a constant number of sampling steps, independent of sequence length. This result demonstrates that efficiency can, in principle, be attained without compromising generation quality. However, when targeting low sequence error rate--which is important for assessing the ``correctness" of a generated sequence, such as a reasoning chain--we show that in the worst case, the required sampling steps must scale linearly with sequence length, thereby eliminating the efficiency advantage. Our analysis establishes the first theoretical foundation for understanding the comparative strengths and limitations of MDMs, offering practical guidance on when to favor MDMs over the auto-regressive models and vice versa.