How do high-trust societies form?

Just speculating here, but if you want to enforce any norms, there must be a way to get rid of the people who refuse to follow them. The question is how, and this depends on the kind of the group.

If the group is something like "people coming to a party I organize", the solution is simply to stop inviting the transgressors. If the group is more like "people living in this village", then you have a problem, because to achieve the same outcome, you would need to exile or kill the transgressors. Which was probably a smaller problem in the past -- if everyone agreed that someone deserves to die, such person simply disappeared one day and no one bothered to investigate how. It is more of a problem today, when the government does not care to protect you efficiently, but suddenly starts paying attention when you take action to protect yourself (because doing so obviously undermines the government's pretext at legitimacy). When the government cares, it can kill people, or "exile" them by putting them in prison.

Okay, I used some harsh words in the previous paragraph. Is "killing (or exiling)" really necessary? Wouldn't a smaller punishment -- such as a fine, or maybe just a concerned frown -- suffice?

I think the answer is: yes it would suffice for most people, but no it wouldn't for some; and you need a clear answer to what happens to those, otherwise your high-trust society still falls apart. If 99% of the population follow the rules but 1% does not, the streets are still littered, homes get broken into, people get raped and murdered. Some people are such that you could fine them out of all the money they have, and they still would keep breaking the rules. So what is the next step here? A civilized solution could be to let them spend their lives in prison. A less civilized solution is to kill them, either officially or unofficially.

So, how do high-trust societies form? At some moment in history, people agree on the rules, and start violently enforcing them. It may be controversial when it happens, but a generation or two later, the rules are simply "how we always do it here". The initial impulse probably comes from a religion or a king (or even from the people, in Switzerland).

How do high-trust societies unravel? When people stop enforcing the rules, for example because the official enforcers of the rules have a conflict of interest, because doing their job properly puts them in bad light somehow (e.g. they get accused of intolerance towards the groups that often break the rules). This naively sounds like diversity is the problem, but the actual problem is when appeasing the diverse groups becomes more important than enforcing the rules. (Singapore is high-trust and diverse.)

Again, this all is just speculation. Historical examples could be very useful, to either support or disprove this.

I'm unclear why you consider low-trust societies to be natural and require no explanation. To me it makes intuitive sense that small high-trust groups would form naturally at times, and sometimes those groups would, by virtue of cooperation being an advantage, grow over time to be big and successful enough to be classed as "societies".

I picture a high trust situation like a functional family unit or small village where everyone knows everyone, to start. A village a few kilometers away is low trust. Over time, both groups grow, but there's less murdering and thievery and expense spent on various forms of protection against adversarial behaviour in the high-trust group, so they grow faster. Eventually the two villages interact, and some members of the low-trust group defect against their neighbours and help the outsiders to gain some advantage for themselves, while the high trust group operates with a unified goal, such that even if they were similarly sized, the high trust group would be more effective. Net result, the high trust group wins and expands, the low trust group shrinks or is exterminated. More generally, I think in a lot of different forms of competition, the high trust group is going to win because they can coordinate better. So all that is needed is for a high-trust seed to exist in a small functional group, and it may grow to arbitrary size (provided mechanisms for detecting and punishing defectors and free-riders, of course).

I don't claim that this is a well-grounded explanation with the backing of any anthropological research, which is why I'm putting it as a comment rather than an answer. But I do know that children often grow up assuming that whatever environment they grew up in is typical for everyone everywhere. So if a child grows up in a functional family that cooperates with and supports each other, they're going to generalize that and expect others outside of their family to cooperate and support each other was well, unless and until they learn this isn't always the case. This becomes the basis for forming high-trust cooperative relationships with non-kin, where the opportunity exists. Seems to me a high trust society is just one where those small seeds of cooperation have grown to a group of societal size. 

Taking it back a step, it seems like we have a lot of instincts that aid us in cooperating with each other. Probably because those with those instincts did better than those without, because a human by itself is puny and weak and can only look in one direction at once and sometimes needs to sleep, but ten humans working together are not subject to those same constraints. And it is those cooperative instincts, like reciprocity, valuing fairness, punishment of defectors, and rewarding generosity with status, which help us easily form trusting cooperative relationships ("easily" relative to how hard it would be if we were fully selfish agents aiming only to maximize some utility function in each interaction, and we further knew that this was true of everyone we interacted with as well), which in turn are the basis for trust within larger-scale groups.

I mean, you're asking this question with the well-founded hope that someone is going to take their own time to give you a good answer, without them being paid to do so or any credible promise of another form of reward. You would be surprised, I think, if the response to this request was an attempt to harm you in order to gain some advantage at your expense. If 10 people with a similar dispositon were trapped on an island for a few generations, you could start a high trust society, could you not?

Speculation only!

it seems that high-trust groups are those that have somewhat homogeneous culture, and strong extended-family and local ties.  In other words, a lot of social enforcement of norms, with less legible codified behavioral limits.  

There can be people who are simultaneously members of high-trust groups and communities, AND low-trust societies and groups.  

The important related question, as you say, can this be arrested or mitigated as a group gets larger and more diverse, so social/cultural norm enforcement via "what will grandma think?" becomes infeasible.