Soft-constraint semi-supervised affinity propagation (SCSSAP) adds supervision to the affinity propagation (AP) clustering algorithm without strictly enforcing instance-level constraints. Constraint violations lead to an adjustment of the AP similarity matrix at every iteration of the proposed algorithm and to addition of a penalty to the objective function. This formulation is particularly advantageous in the presence of noisy labels or noisy constraints since the penalty parameter of SCSSAP can be tuned to express our confidence in instance-level constraints. When the constraints are noiseless, SCSSAP outperforms unsupervised AP and performs at least as well as the previously proposed semi-supervised AP and constrained expectation maximization. In the presence of label and constraint noise, SCSSAP results in a more accurate clustering than either of the aforementioned established algorithms. Finally, we present an extension of SCSSAP which incorporates metric learning in the optimization objective and can further improve the performance of clustering.