Note: If you think the assertion is obvious, then this post may well not interest you.

A bit of terminology: The original scientific definition of pedophile is someone with a strong sexual attraction to prepubescent children. In law enforcement and the popular press, it is also used to refer to a person who seeks sexual activity with a minor, very often one who is sexually mature in the 13-17 range. The idea of a celibate pedophile of this second kind doesn't really make sense, except perhaps to a few people who think it is unusual for men to feel sexual attraction to young teens. In what follows I refer to the first.

Many people in society think celibate pedophiles either don't exist or are a negligible minority of all pedophiles.

One reason they think that is that pedophiles very rarely "out" themselves voluntarily -- the ones that society knows about are those who have been investigated for child sex abuse or for child pornography possession. Well-intentioned scientists, therapists, and law enforcement personnel all generalize about pedophiles based on those who break the law. It is one of the most spectacular examples of a biased sample problem that I can think of. Yet this near-certainty of sample bias doesn't address how many people there actually are in the under-sampled group.

The reluctance of pedophiles to "out" themselves also means that we celibate pedophiles are also in a poor position to judge our numbers. Pedophiles have banded together on the internet since its inception in anonymous communities. One focus of such communities is exchanging child pornography. Another common focus is decrying how unfair society is to not allow adult-child sex -- though many other people in such groups are against legalizing adult-child sex. Many members of these groups will claim that they never engage in sexual activity with children, but there are reasons that they might lie. For one thing, they might not want to invite attention from law enforcement if they feel their online anonymity is not secure. For another, the forum rules might prohibit discussing it. What percentage of such people are lying is an important unknown. A much larger problem is that generalizing from those who discuss something online to prevalence in the population is difficult.

There is some indirect evidence that could be brought to bear. Seto et al did a meta-analysis of men who were arrested for child porn offenses and for contact offenses with children:

http://www.theroyal.ca/wp-content/uploads/2013/07/2011_Seto_Contact-Sexual-Offending-by-Men-With-Online-Sexual-Offenses.pdf

They found that of men who were arrested for a child porn offense, about half had either admitted a past contact offense or were arrested for a past or future contact offense.

This suggests a substantial group of men who are strongly attracted to children sexually but who do not abuse them.

One alternative explanation could be that all the men caught with child porn also abuse children, it's just that they have not been caught for the latter crime. This seems unfair, since the implicit control group of non-pedophiles also might have abused children and not been caught. In fact, a great deal of sex abuse is perpetrated by men who are primarily attracted to adults, but who abuse a child because she or he is available and they have some measure of attraction. It's hard for anyone to prove that they do not abuse children.

So we have a substantial group of pedophiles who do not abuse children. The existence of this group has important policy implications (beyond the scope of this post). Of course society will still take a dim view of child porn offenders. There are also pedophiles who are not only celibate but do not look at child porn. Can we go further and draw any inferences about how frequent the totally law-abiding pedophiles are?

If among the population of all pedophiles we consider the cross-product of those who are guilty of child porn offenses and those who aren't, with those who are guilty of contact offenses and those who are not, the studies that Seto summarizes have 3 of the 4 groups. It would be surprising if the fourth group was empty or tiny in size. If the tendency to commit one crime was independent of the tendency to commit the other, we could estimate the size of this group; it would be of roughly the same magnitude as the other three groups. (Someone more incisive than me might be able to do some calculations based on the data in Seto's paper.) However, one would expect a strong positive correlation between breaking one law related to one's sexual desires and breaking the other. We might expect a large number of men to be committed to not breaking any laws with serious penalties.

This analysis certainly allows for a large population of pedophiles who neither abuse children nor view child porn.

We can also try to look at this more intuitively. Everyone knows that child sex abuse is one of society's strongest taboos -- it is nearly universally regarded as a terrible moral failure. Most people don't violate such taboos. It's also a crime punished by severe penalties, and most people don't commit such crimes if they think they might be caught. What extraordinary features might pedophiles have that would lead society to think that almost all of them would commit such a crime? One is that sex is a strong drive, and pedophiles have no legal outlets for their desires. For a comparison I would suggest ordinary men who for whatever reason can't get a date and don't visit prostitutes. I suggest that the vast majority of such men are not rapists.

Another possibility is that pedophilia is highly correlated with severe deficits in impulse control, empathy, or moral reasoning. No such strong relationships are known, because no one has studied celibate pedophiles. One comparison scientists can make is between sex offenders against children and sex offenders against adults. There are minor differences (such as offenders against children being less intelligent), but nothing major -- nothing that would support a hypothesis that 98% of ordinary men are not sex offenders but only (say) 40% of pedophiles are not.

There are apparently a set of "antisocial" features associated with all criminals, and they are also found in child sex abusers. (An interesting result is that child-porn-only offenders do not have those same antisocial traits.)