Id disagree.
There are vast numbers of Pedophiles who never progress beyond the desire stage (looking at images etc) and more still who suppress their urges entirely.
What makes some Pedophiles progress to the actual abuse of children is probably not dissimilar to the progression of a Rapist - and narcissism is a common trait assigned to Rapists which would suggest that the willingness to act on their urges is separate from their sexual desires.
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