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We address the question of constructing practical blind watermark decoders that are resilient to scaling and amplitude modulation attacks. We cast the watermark decoding problem as a probabilistic inference problem on a factor graph and solve it via message passing. Our decoder performs nearly as well as a decoder that has exact knowledge of the desynchronization parameters. Experimental results, on both synthetic and natural images, suggest that the decoding algorithm is capable of handling moderate to strong desynchronization attacks very well.