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We present an incremental refinement algorithm for approximate compilation of constraint satisfaction models into multivalued decision diagrams (MDDs). The algorithm uses a vertex splitting operation that relies on the detection of equivalent paths in the MDD. Although the algorithm is quite general, it can be adapted to exploit constraint structure by specializing the equivalence tests for partial assignments to particular constraints. We show how to modify the algorithm in a principled way to obtain an approximate MDD when the exact MDD is too large for practical purposes. This is done by replacing the equivalence test with a constraint-specific measure of distance. We demonstrate the value of the approach for approximate and exact MDD compilation and evaluate its benefits in one of the main MDD application domains, interactive configuration.