What is the Buddhist perspective on child abuse? Suppose a father is abusing his 3 year old child. As a consequence, the child is suffering. Who is the cause of the child's suffering?
The Pali scriptures (SN 12.17) state, from the perspective of ultimate truth, that the cause of suffering is 'ignorance' (rather than 'one-self' or 'another'). 

However, in the conventional scenario presented in the question, the father is causing the suffering because a 3 year old child does not have the cognitive capacity to engage the Buddhist path. 

What is occurring to the child has no relationship to any (imaginary) past lives. I have never read this idea in the Pali suttas, where suffering (dukkha), let alone the suffering of helpless small children, is attributed to past lives. 

The suffering is due to the evil within the mind of the father because the child cannot overcome the in-born ignorance in their mind that is causing the suffering.

Dhammapada 137 clearly states there are "innocent" victims of crime &amp; AN 3.61 states what a person feels in not related to past kamma. 


  137. He who inflicts violence on those who are unarmed and offends those who are inoffensive, will soon come upon one of these ten
  states:
  
  138-140 Sharp pain, or disaster, bodily injury, serious illness, or derangement of mind, trouble from the government, or grave charges,
  loss of relatives, or loss of wealth, or houses destroyed by ravaging
  fire; upon dissolution of the body that ignorant man is born in
  hell.


~~~


  When one falls back on what was done in the past as being essential, monks, there is no desire, no effort [at the thought], 'This should be
  done. This shouldn't be done.' When one can't pin down as a truth or
  reality what should &amp; shouldn't be done, one dwells bewildered &amp;
  unprotected. One cannot righteously refer to oneself as a
  contemplative. This was my first righteous refutation of those
  brahmans &amp; contemplatives who hold to such teachings, such views.