Large language model (LLM)-powered multi-agent systems (MAS) demonstrate remarkable collective intelligence, with multi-agent memory serving as a pivotal mechanism for continual adaptation. However, existing multi-agent memory designs remain constrained by two fundamental bottlenecks: (i) memory homogenization caused by limited role-aware customization, and (ii) information overload induced by exposing agents to excessively fine-grained textual memories. To address these limitations, we propose LatentMem, a learnable multi-agent memory framework that customizes agent-specific experiential memories while reducing textual context. Specifically, LatentMem comprises an experience bank for lightweight storage of raw interaction trajectories and a memory composer that synthesizes compact latent memories conditioned on retrieved experience and agent-specific contexts. Further, we introduce Latent Memory Policy Optimization (LMPO), which propagates task-level optimization signals through latent memories to learn compact, high-utility latent representations. Extensive experiments across six benchmarks and four mainstream MAS frameworks show that LatentMem improves vanilla settings by up to 19.36% and consistently outperforms existing memory architectures, without requiring modifications to the agent-layer workflows.