why speculative decoding's output distribution is guaranteed to stay the same? speculative sample [Research]

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https://preview.redd.it/fk76iuoan2dc1.png?width=357&format=png&auto=webp&s=7b909330a6ccf70258e620c2cc1cfdfa11ee4c40

https://preview.redd.it/n78eend9n2dc1.png?width=353&format=png&auto=webp&s=316b4b74fed8360b5d83845a20f757d9331d131b

q(x) is draft model

p(x) is original, target model

I don't understand why after the speculative decoding algorithm the output distribution is the same as target model distribution, for example:

1. why keeping xi if q(xi) <= p(xi) will not change the output distribution from target model?
2. why we need sample x again from norm(max(0,p(x) -q(x) ) if x was rejected
1. and why normalized p(x) is not changing the distribution from target model?

really appreciate …

algorithm change decoding decoding algorithm distribution draft example machinelearning research sample will