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.

Large Language Models struggle with memory demands from the growing Key-Value (KV) cache as context lengths increase. Existing compression methods homogenize head dimensions or rely on attention-guided token pruning, often sacrificing accuracy or introducing computational overhead. We propose FourierAttention, a training-free framework that exploits the heterogeneous roles of transformer head dimensions: lower dimensions prioritize local context, while upper ones capture long-range dependencies. By projecting the long-context-insensitive dimensions onto orthogonal Fourier bases, FourierAttention approximates their temporal evolution with fixed-length spectral coefficients. Evaluations on Llama and Qwen models show FourierAttention achieves the best long-context accuracy on LongBench and Needle-In-A-Haystack (NIAH). Besides, a custom Triton kernel, FlashFourierAttention, is designed to optimize memory via streamlined read-write operations, enabling efficient deployment without performance compromise.