A Convergence Theory for Diffusion Language Models: An Information-Theoretic Perspective
This provides foundational theoretical insights for researchers in generative modeling, addressing a key gap in understanding diffusion models for language tasks.
The paper tackled the lack of theoretical understanding for diffusion language models by developing convergence guarantees from an information-theoretic perspective, showing that sampling error decays inversely with iteration count and scales linearly with token mutual information, with matching upper and lower bounds.
Diffusion models have emerged as a powerful paradigm for modern generative modeling, demonstrating strong potential for large language models (LLMs). Unlike conventional autoregressive (AR) models that generate tokens sequentially, diffusion models enable parallel token sampling, leading to faster generation and eliminating left-to-right generation constraints. Despite their empirical success, the theoretical understanding of diffusion model approaches remains underdeveloped. In this work, we develop convergence guarantees for diffusion language models from an information-theoretic perspective. Our analysis demonstrates that the sampling error, measured by the Kullback-Leibler (KL) divergence, decays inversely with the number of iterations $T$ and scales linearly with the mutual information between tokens in the target text sequence. In particular, we establish matching upper and lower bounds, up to some constant factor, to demonstrate the tightness of our convergence analysis. These results offer novel theoretical insights into the practical effectiveness of diffusion language models.