Despite the non-autoregressive potential of diffusion language models (dLLMs), existing decoding strategies exhibit positional bias, failing to fully unlock the potential of arbitrary-order generation. In this work, we delve into the inherent spectral characteristics of dLLMs and present the first frequency-domain analysis of dLLMs, showing that low-frequency components in hidden states primarily encode global structural information and long-range dependencies, while high-frequency components capture local details. Based on this observation, we propose FourierSampler, which leverages a frequency-domain sliding window mechanism to dynamically guide the model to achieve "structure-to-detail" generation. FourierSampler outperforms other inference enhancement strategies on LLaDA and SDAR, achieving relative task-specific gains up to 20.4% on LLaDA-1.5 and 16.0% on LLaDA-8B-Instruct, as well as average gains up to 8.6% across tasks.

Language model heavily depends on high-quality data for optimal performance. Existing approaches rely on manually designed heuristics, the perplexity of existing models, training classifiers, orcareful prompt engineering, which require significant expert experience and human annotation effort while introduce biases. We introduce CritiQ, a novel data selection method that automatically mines criteria from human preferences for data quality with only ~30 human-annotated pairs and performs efficient data selection. The main component, CritiQ Flow, employs a manager agent to evolve quality criteria and worker agents to make pairwise judgments. We build a knowledge base that extracts quality criteria from previous work to boost CritiQ Flow. Compared to perplexity- and classifier-based methods, verbal criteria are more interpretable and have greater reusable value. After deriving the criteria, we train the CritiQ Scorer to give quality scores and perform efficient data selection. We demonstrate the effectiveness of our method in the code, math, and logic domains, achieving high accuracy on human-annotated test sets. To validate the quality of the selected data, we continually train Llama 3.2 models and observe improved performance on downstream tasks compared to uniform sampling. Ablation studies validate the benefits of the knowledge base and the reflection process. We analyze how criteria evolve and the effectiveness of majority voting.