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In this paper, we consider the transmission of a Gaussian source over a cooperative relay network, and analyze its end-to-end distortion at high signal-to-noise ratio, in terms of the distortion exponent. Our contributions are threefold. First, we extend the existing distortion exponent analyses to cooperative networks with an arbitrary number of relays. Second, we derive the distortion exponents when the layered source coding with broadcast transmission strategy is used in multi-relay networks under three cooperation protocols, based on repetition, relay selection, and space-time coding, respectively. Our analyses reveal the impacts of the number of relays, bandwidth ratio and cooperation protocol on the distortion exponent. Third, we prove the successive refinability of the diversity-multiplexing tradeoffs of the three multi-relay cooperation protocols.