Generative Recommendation (GR) has exhibited great potential by modeling item transitions as a sequence-to-sequence task. Despite the success of GR, existing frameworks primarily focus on modeling individual user sequences within a constrained internal parametric space, failing to explicitly leverage cross-user collaborative signals. To address this issue, we propose \textbf{OMEGA}, a cOllaborative MEmory augmentation framework for Generative recommendAtion. OMEGA bridges the gap between implicit parametric knowledge and explicit collaborative signals. We first introduce a latent context compression method that utilizes learnable query tokens to distill sequential user behavior into compact representations, significantly reducing storage overhead. These compressed representations are aggregated into a collaborative memory bank, serving as an explicit repository of global behavioral patterns. To ensure precise knowledge acquisition, we design a lightweight and target-aware retrieval mechanism that identifies pertinent memories by considering both sequence-level and target-level similarities. Furthermore, a context-aware integration module, equipped with a gated cross-attention mechanism, is employed to adaptively fuse the retrieved collaborative memories with the local user context while mitigating the interference of noisy patterns. Empirical evaluations on multiple real-world datasets demonstrate that OMEGA significantly outperforms existing advanced GR models, validating the potential of external memory as a complement to the generative paradigm.

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