Give them a chance.
Seriously.
There is a horrifying stigma against these people, and for good reason - I'm no about to condone their actions or even suggest it's acceptable in any way, it's certainly one of the most heinous acts a human can do.
But.
The way they are treated is often disproportionate to a civilized society of human rights and understanding.
Let me explain. It is natural for most of us to think along the lines of 'anybody who thinks about a little boy or girl like that is sick, twisted and evil. They need to be put to death, they will serve no purpose in our society'.
There are many problems with this argument though:
Culture
In Nigeria, the legal age of sexual consent is 11. 'The age of consent is 12 in the Philippines and Angola, and 13 in Burkina Faso, Comoros, Niger, and Japan'. Japan is considered the only developed country with such a law, but local states change that age to a more updated range of 16-18.
Does this imply that paedophilia is simply in the minds of our developed, educated societies? Maybe. But why? Is it wealth, health, education, religion that created taught us somehow sex with children is wrong? Why would an undeveloped town or village decide that it's actually ok? In many countries, some more developed than others (ok the middle east), there is no consent age at all:
'...in some countries girls are married at as young as 9 or 10 years old. Countries with marriage-based ages of consent include Afghanistan, Iran, Kuwait, Libya, Maldives, Oman, Pakistan, Qatar, Sudan, Saudi Arabia, Yemen, and the UAE'. Some of these countries limit their marriage ages, such as Yemen at 15, Iran at 13. Aside from the very questionable ethics behind child marriage, everything beyond that is also fair game.
Why were these laws put in at this age? Surely, if Paedophilia is just the devil's work and pure evil, any laws set in place worldwide would make effort to stop it. In the same way that there were laws preventing homosexuality.
Being gay was and indeed still is a crime and considered a heinous act against God in many countries (74 out of 196, in fact - almost 40% of countries worldwide). But from our high horses in the west, we look down on these countries and consider THOSE the sick individuals who just have no idea how biology works. Well, let's look into biology later.
History
Let's go back in time, way back before civilisation, tens of thousands of years, in a time where survival was priority. At this point, physical maturity far out-ranked mental maturity. A girl typically becomes sexually mature around 10-12 years old (and in the modern day, puberty is happening earlier and earlier), with one girl documented getting pregnant at the age of 5.
Why would a small group of human-like beasts care about a girl's mental wellbeing? Have you ever seen a cat or a duck have sex? it isn't pretty, and it happens within days of sexual maturity. Those instincts are likely still in us somewhere, suppressed.
Of course it's good that this urge is suppressed because we are no longer human-like beasts, but it's evidence to suggest that it is not some kind of biological freak show; in fact, it seems that having sex at such a young age is actually pretty normal, in the grand scheme of the tree of life.
When you think about groups of animals, you typically think of alpha males. Sure, a 12 year old boy might have sex with a 12 year old girl and that doesn't seem SO bad, just stupid, but in a tribe, it would be the alpha male that gets all the girls, and an alpha male is unlikely to be a little teenage boy, but in fact a full grown, experienced and mature adult.
Science
As mentioned above, homosexuality has historically been outlawed and almost half the world still considers it a crime. Education and ethics have changed for us, but could it change for paedophilia? Let's look at the science first.
There is a lot of evidence to show that the early stages of brain growth are substantially affected in a pedophile:
Perhaps most striking of all, pedophiles were less likely to be right-handed. 8 to 12 percent of the population is left-handed or ambidextrous. In the pedophiles that Cantor studied, a third of them were...Further research led to discoveries that pedophiles tended to do poorly on memory tests. They also tended to be shorter in stature than teleiophiles, as if the whole body was not formed correctly. They were more likely to have failed grades in school, and to have suffered from head injuries before the age of 13'
The left hemisphere of the brain will normally develop faster than the other side, which leads to the majority of right-handed people, but when development is altered in some way and that development slows, the brain compensates with the right hemisphere and you get a left-handed individual. Left-handedness could indeed be a small clue to the source of pedophilia, be it a developmental problem in-utero or otherwise.
One theory suggested that pedophiles had issues with their temporal lobe, which controls our most basic survival motivations, or the four F's: "feeding, flight, fighting, and fornicating". This is where I think it gets particularly interesting, and leads back to our History section above.
If the temporal lobe has been affected then that fourth F, f***ing, could have problems being suppressed according today's basically unnatural laws of ethics. There is also some ideas that wires are being crossed in the white matter of their brains, causing a naturally protective instinct to cross with sexual instinct. There's a whole lot to read about here which you can check in the link below.
Society
Well, if there's a scientific approach, can we 'cure' it? Well, I think that's the wrong question. Many religious folk around the world ask that same question about homosexuality. We are learning to not consider gayness an 'illness' and simply just another version of a regular person. But society causes a lot of pain, anguish and torment for the LGBT community, often leading to suicides, murders, depression and more.
40% of transgenders, for example, will attempt suicide and generally be suicidal, as a result of their families rejecting them, a lack of social support, living in poverty because they cannot find an accepting job, people abusing them in the streets and so on. Society is not ready for LGBTs yet.
This same stigma is, naturally, applied to pedophiles. Where can a pedophile live? Where can they work? Who can they be friends with? The answer to all is generally nowhere, nowhere, nobody. Many pedophiles are homeless, with no graduation under their belt, no career prospects. They are often starved or murdered in prison, and inevitably, escape to countries like the Philippines to do their deeds in the dark web where they are safest.
Suicide attempts among non-offending pedophiles is thought to be as high as 90%.
So does society contribute to the prevention of pedophilia, or does it in some way encourage it? I would argue the latter. Louis Theroux's documentary, 'A place for pedophiles' explores these individuals very personally and up close. He finds that, in the asylum he visited, many of them didn't actually commit a crime at all, and in fact voluntarily gave themselves up, with the full understanding that who they are has no place in society and they do not want to be a risk or a danger to anybody. Some of them voluntarily have themselves castrated in a desperate attempt to convince society that he is safe now and he can live among them. 
None of them claim they are 'cured', however, but they insist that they have control over themselves like any other man, gay, trans or otherwise. This reminds me a little of the whole transgender bathroom debacle, as if MTF trans individuals are all sexual predators who want to sneak into bathrooms to take little girls. It's an ignorant approach to human nature.
Most of the pedophiles in this documentary never get to see the outside world again, and even those admitted for release never find a neighborhood willing to accept them.
Do the above sound like people who are 'sick, twisted and evil who need to be put to death because they will serve no purpose in our society'? I don't think so.
For those who commit or attempt a crime like this, of course, they need to be punished big time. But if we demonize it to such an extent that our ears are closed and our baseball bats are out, we are doing nothing but drive them underground, and encouraging them to pursue their urges.
When there is so much Culture, History, Science and Sociological reasons that pedophilia is perpetuated, You've gotta take a step back and think; what's the best course of action here?
For me, curing them is not an option. Imprisoning them pre-crime is not an option. Brainwashing or lobotomizing them is not an option. These all go against the human rights we live by in the modern world.
The best action, in my opinion, is:
Learn and prevent. Science is showing there are developmental causes leading to pedophilia. Showing understanding of the subject can be valuable for society as a whole, and possibly lower the number of future pedophiles growing up.
Teach. Have a place where an otherwise innocent pedophile can go for help, to be away from those who are too young to consent and can eventually learn to contribute to society in other ways. In some European countries, drug addicts have free facilities and nurses to help them inject their heroine. Not because they agree that it's a cool thing to do, but because when they are driven underground, they end up with dirty needles, HIV and the spread thereof. These countries understand that there is no winning a drug war, but you can minimize the related death. The same concept should apply to pedophiles.
Thoughts?
Sources:
https://www.ageofconsent.net/highest-and-lowest
http://www.sciencealert.com/girls-are-going-through-puberty-earlier-than-ever-before-with-long-term-effects
http://www.medicaldaily.com/science-pedophilia-it-sexual-orientation-242403