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Traditional image and video compression algorithms rely on hand-crafted encoder/decoder pairs (codecs) that lack adaptability and are agnostic to the data being compressed. We describe the concept of generative compression, the compression of data using generative models, and suggest that it is a direction worth pursuing to produce more accurate and visually pleasing reconstructions at deeper compression levels for both image and video data. We also show that generative compression is orders- of-magnitude more robust to bit errors (e.g., from noisy channels) than traditional variable-length coding schemes.