Masked diffusion language models (DLMs) generate text through iterative parallel decoding, but at low step budgets, committing many tokens independently can produce premature termination or repetitive outputs. Continuous embedding-space denoising can mitigate this failure mode by maintaining soft states for all positions, yet training such models from scratch at scale remains challenging. We show that a pretrained masked DLM can instead be efficiently adapted to support continuous denoising. Starting from LLaDA-8B-Instruct, we perform only 1,000 steps of continued pretraining with Discrete Stochastic Localization (DSL), replacing binary masking with continuous per-token Gaussian noise mapped to soft embedding mixtures. The adapted model supports SDE-based inference that evolves all positions jointly and defers hard token commitment to the final step. At ≤16 denoising evaluations, DSL-LLaDA substantially mitigates the premature-termination and repetition tradeoff in open-ended generation and achieves the best ROUGE-1 among the evaluated diffusion baselines on all four zero-shot summarization benchmarks. The same adaptation also enables selective correction of corrupted tokens while preserving more than 98% of clean tokens. Same-compute controls indicate that these behaviors arise from continuous-noise exposure rather than additional training alone.

Key-Value (KV) cache compression techniques have improved the efficiency of long-context summarization in Large Language Models (LLMs), but their impact on model hallucination remains underexplored. In this paper, we present the first systematic study of how KV cache compression affects hallucination in long-context summarization, demonstrating that aggressive compression can increase hallucination scores by up to 3.36× compared to the baseline. To mitigate this issue, we propose HalluKV, a decoding-phase strategy that selectively removes generated KV pairs from retrieval heads responsible for retrieving critical information from source context, thereby anchoring their attention on the preserved source information. Our approach maintains computational efficiency while significantly reducing hallucination across multiple models and datasets, achieving up to 5.48 average point reductions on Llama-3-8B-Instruct, enabling more trustworthy long-context summarization.