For a deterministic block cipher, can two different inputs ever produce the same output?

Take a block cipher with input K, M. I understand that block ciphers are deterministic and will always produce the same output X when given the same values for inputs K and M.

However, given a block cipher with input K1, M1 and output X1 and one with input K2, M2 and output X2, is it ever possible that X1 = X2 is true?

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