We consider the problem of a set of nodes which is required to collectively learn a common dictionary from noisy measurements. This distributed dictionary learning approach may be useful in several contexts including sensor networks. Dif-fusion cooperation schemes have been proposed to estimate a consensus solution to distributed linear regression. This work proposes a diffusion-based adaptive dictionary learning strategy. Each node receives measurements which may be shared or not with its neighbors. All nodes cooperate with their neighbors by sharing their local dictionary to estimate a common representa-tion. In a diffusion approach, the resulting algorithm corresponds to a distributed alternate optimization. Beyond dictionary learn-ing, this strategy could be adapted to many matrix factorization problems in various settings. We illustrate its efficiency on some numerical experiments, including the difficult problem of blind hyperspectral images unmixing.