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Normal language models generate one token per forward pass, which is slow because each step must wait for the previous one. Medusa adds lightweight feed-forward heads on top of the frozen base model; each head predicts a token a few positions ahead (head 1 predicts the next token, head 2 the token after, and so on). These predictions form a tree of candidate continuations. The full model then verifies the whole tree in one pass using a 'tree attention' mask, accepting the longest prefix that matches what the model would have produced anyway. For Medusa-1, the backbone stays frozen and original-model rejection sampling can preserve the base model's output distribution, enabling lossless inference acceleration. Medusa-2 jointly trains the heads and backbone with a special recipe that preserves the backbone's next-token capability while improving head prediction. The paper also studies typical acceptance, which can increase acceptance and maintain similar generation quality but does not make the same exact distribution-matching guarantee.