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We propose a new paradigm for blind watermark decoding in the presence of desynchronization attacks. Employing Forney-style factor graphs to model the watermarking system, we cast the blind watermark decoding problem as a probabilistic inference problem on a graph, and solve it via message-passing. We study a wide range of moderate to strong attacks including scaling, amplitude modulation, fractional shift, arbitrary linear and shift-invariant filtering, and blockwise filtering, and show that the graph-based iterative decoders perform almost as well as if they had exact knowledge of the desynchronization attack parameters. Other desirable features of the graph-based decoders include the flexibility to adapt to other types of attacks and the ability to cope with the “curse of dimensionality” problem that seemingly results when the desynchronization parameter space has high dimensionality. These properties are unlike most blind watermark decoders proposed to date.