arXiv:2509.25035v1 Announce Type: cross Abstract: Fast generation of language texts is the holy grail that people pursue in the AI era. In this work, we introduced Discrete Diffusion Divergence Instruct (DiDi-Instruct), a training-based method that leads to fast language generation models by initializing from a pre-trained (masked) discrete diffusion language model (dLLM). The resulting DiDi-Instruct model outperforms the dLLM counterparts and the GPT-2 baseline with 64x acceleration. In the theoretical part of the paper, we build the foundation of DiDi-Instruct in a framework of integral KL-divergence minimization, with practical training algorithms. We also introduce techniques like grouped reward normalization, intermediate-state matching, and the reward-guided ancestral sampler (RGAS) that significantly improve the training stability, the model coverage, and the inference performances. On OpenWebText, DiDi-Instruct outperforms all accelerated language generation models as well as the GPT-2 baseline and the standard dLLMs, achieving sample perplexities ranging from 62.2 (8 NFEs) to 18.4 (128 NFEs). These performance gains are accomplished with a negligible entropy loss of about 1% and 20x less additional training wall-clock time. We further validate the robustness and effectiveness of DiDi-Instruct through extensive ablation studies, model scaling, and the generation of discrete protein sequences. In conclusion, DiDi-Instruct is an efficient yet effective distillation method, enabling language generation in the blink of an eye. We will release both code and models at github.com/haoyangzheng-ai/didi-instruct.