Efficient long-context inference remains a major challenge for large language models (LLMs), as the cost of attention computation during auto-regressive decoding grows linearly with the context length.Recent sparse attention methods attempt to reduce the computational burden by selecting a subset of tokens at each step, while most rely on static importance scores that are repeatedly computed over the entire cache, overlooking the relational dynamics of the decoding process.In this work, we revisit sparse attention in LLMs and propose to model token importance as a dynamic process that evolves over decoding steps and propagates through model layers.To efficiently measure token importance, we propose two lightweight mechanisms: (1) Cross-Step Accumulation, which incrementally maintains long-term, query-agnostic importance via decayed accumulation of sparse attention scores, avoiding recomputing the importance of decoded tokens; and (2) Cross-Layer Propagation, which leverages the model's intrinsic Retrieval Heads to compute query-aware indices and efficiently propagate them across layers; Together, these mechanisms preserve both stable context memory and adaptive query relevance while reduce redundant computation.We evaluate our approach on PG-19, RULER, LongBench, and mathematical reasoning benchmarks using models employing Multi-Head and Grouped-Query Attention.Under varying KV cache budgets, our method consistently outperforms prior sparse attention baselines, approaches full attention performance in most settings, and achieves speedups of up to 5.36× for attention latency and 2.33× for end-to-end decoding.Our code is available at: https://github.com/iLearn-Lab/ACL26- EvoSparse.