In this letter, we propose a six-dimensional movable antenna (6DMA)-aided cell-free massive multiple-input multiple-output (MIMO) system to fully exploit its macro spatial diversity, where a set of distributed access points (APs), each equipped with multiple 6DMA surfaces, cooperatively serve all users in a given area. Connected to a central processing unit (CPU) via fronthaul links, 6DMA-APs can optimize their combining vectors for decoding the users' information based on either local channel state information (CSI) or global CSI shared among them. We aim to maximize the average achievable sum-rate via jointly optimizing the rotation angles of all 6DMA surfaces at all APs, based on the users' spatial distribution. Since the formulated problem is non-convex and highly non-linear, we propose a Bayesian optimization-based algorithm to solve it efficiently. Simulation results show that, by enhancing signal power and mitigating interference through reduced channel cross-correlation among users, 6DMA-APs with optimized rotations can significantly improve the average sum-rate, as compared to the conventional cell-free network with fixed-position antennas and that with only a single centralized AP with optimally rotated 6DMAs, especially when the user distribution is more spatially diverse.
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