In the past decade, significant progress has been achieved in developing generic primal heuristics that made their way into commercial mixed integer programming (MIP) solver. Extensions to the context of a column generation solution approach are not straightforward. The Dantzig-Wolfe decomposition principle can indeed be exploited in greedy, local search, rounding or truncated exact methods. The price coordination mechanism can bring a global view that may be lacking in some ''myopic'' approaches based on a compact formulation. However, the dynamic generation of variables requires specific adaptation of heuristic paradigms. The column generation literature reports many application specific studies where primal heuristics are a key to success. There remains to extract generic methods that could be seen as black-box primal heuristics for use across applications. In this paper we review generic classes of column generation based primal heuristics. We then focus on a so-called ''diving'' method in which we introduce diversification based on Limited Discrepancy Search. While being a general purpose approach, the implementation of our heuristic illustrates the technicalities specific to column generation. The method is numerically tested on variants of the cutting stock and vehicle routing problems.