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Intelligent reflecting surfaces (IRSs) have emerged as a promising economical solution to implement cell-free networks. However, the performance gains achieved by IRSs critically depend on smartly tuned passive beamforming based on the assumption that the accurate channel state information (CSI) knowledge is available, which is practically impossible. Thus, in this paper, we investigate the impact of the CSI uncertainty on IRS-assisted cell-free networks. We adopt a stochastic programming method to cope with the CSI uncertainty by maximizing the expectation of the sum-rate, which guarantees robust performance over the average. Accordingly, an average sum-rate maximization problem is formulated, which is non-convex and arduous to obtain its optimal solution due to the coupled variables and the expectation operation with respect to CSI uncertainties. As a compromising approach, we develop an efficient robust joint design algorithm with low-complexity. Particularly, the original problem is equivalently transformed into a tractable form, and then, the locally optimal solution can be obtained by employing the block coordinate descent method. We further prove that the CSI uncertainty impacts the design of the active transmitting beamforming of APs, but surprisingly does not directly impact the design of the passive reflecting beamforming of IRSs. It is worth noting that the investigated scenario is flexible and general, and thus the proposed algorithm can act as a general framework to solve various sum-rate maximization problems. Simulation results demonstrate that IRSs can achieve considerable data rate improvement for conventional cell-free networks, and confirm the resilience of the proposed algorithm against the CSI uncertainty.