Time Series Foundation Models (TSFMs) achieve strong zero-shot forecasting through large-scale pre-training, but adapting them to downstream domains under distribution shift remains challenging. Existing solutions face a trade-off: Parametric Adaptation can cause catastrophic forgetting and requires costly multi-domain maintenance, while Non-Parametric Retrieval improves forecasts but incurs high inference latency due to datastore search. We propose Parametric Memory Distillation and implement it as TS-Memory, a lightweight memory adapter that augments frozen TSFMs. TS-Memory is trained in two stages. First, we construct an offline, retrieval-leakage-safe kNN teacher that synthesizes confidence-aware quantile targets from retrieved futures. Second, we distill this retrieval-induced distributional correction into a lightweight memory adapter via confidence-gated supervision. During inference, TS-Memory fuses memory and backbone predictions with constant-time overhead, enabling retrieval-free deployment. Experiments across diverse TSFMs and benchmarks demonstrate consistent improvements in both point and probabilistic forecasting over representative adaptation methods, with efficiency comparable to the frozen backbone. Code: https://github.com/sisuolv/TS-Memory.

翻译：时间序列基础模型（TSFMs）通过大规模预训练实现了强大的零样本预测能力，但在分布偏移场景下将其适配至下游领域仍具挑战性。现有方案面临性能权衡：参数化适配方法可能引发灾难性遗忘并需昂贵多域维护成本，而非参数化检索方法虽能提升预测效果却因数据库搜索导致高推理延迟。我们提出参数化记忆蒸馏方法，并实现为TS-Memory——一种轻量级记忆适配器，用于增强冻结的TSFMs。TS-Memory采用两阶段训练：首先构建离线的、无检索泄漏风险的k近邻教师模型，通过检索未来信息合成置信感知分位数目标；其次通过置信门控监督机制，将检索诱导的分布校正知识蒸馏至轻量级记忆适配器中。推理时，TS-Memory以恒定时间开销融合记忆与骨干网络预测结果，实现免检索部署。跨多种TSFMs与基准的实验表明，该方法在点预测与概率预测任务上均显著优于代表性适配方法，且效率与冻结骨干网络相当。代码：https://github.com/sisuolv/TS-Memory。