If your goal is having no collisions then there is a simple strategy that does is at the expense of having many collisions if there are any:
You have a large number of processes that generate UUIDs. For example my computer might be one such process. Each process generates one random UUID, and from then on returns the next UUID every time. If two processes each generate a million UUIDs then you get a collision only if the initial UUIDs are less than a million apart. However, if you have one collision, you will have many. The probability to have any collision at all is much smaller. The expected number of collisions is exactly the same as with random UUIDs. What is very important is that the first random number is truly 128 bits or more.