Cell-free Massive multiple input and multiple output (MIMO) is recognized as a key technology for beyond-5G networks, where distributed access points (APs) jointly serve user equipments (UEs) to address the inherent inter-cell interference issue inherent in cellular systems. While conventional distributed signal detection methods offer a practical balance between performance and fronthaul load, they are fundamentally limited by linear processing constraints. In this paper, we propose a novel deep learning based uplink detection framework by introducing the distributed mixture of experts detection network (DMoE-DetNet). In this architecture, each AP acts as a local expert employing convolutional neural networks (CNNs) for non-linear feature extraction, and transmits the local minimum mean square error (MMSE) detection results and statistical channel information to the central processing unit (CPU). In the CPU, an attention-based encoder module captures complex spatio-temporal dependencies among users for global feature fusion, with a gating network at the central processor dynamically weighting the contributions from different APs. At last, a linear detector outputs the symbol probability. Simulation results demonstrate that the proposed DMoE-DetNet significantly outperforms conventional linear processing based cell-free signal detection methods in terms of symbol error rate, showcasing the potential of artificial intelligence-enabled communication systems.