I have much better luck just letting nature take its course with most difficult to germinate plants such as bleeding hearts, peonies and hellebores than I do trying to germinate them deliberately. With most of these I only want modest numbers of them anyway so that is not a problem.
Of course, there are always exceptions. I was never able to get sweet ciciely going at my house without sowing them in a seed bed over the winter and then transplanting them. I now can't get rid of the stuff and my peerless gardening partner claims it has become a weed. On the other hand, I fussed and fussed to germinate Hellebores and find they grow like weeds beneath any mature plant.
I searched everywhere for a Henry Mitchell quote about this stuff and finally found it by doing a web search. Of course, if I'd never read the whole Henry Mitchell book to begin with I wouldn't have known what to search for. I searched for "Henry Mitchell I have so many weeds", the quote is on the second page of 'A Word About Worts' in One Man's Garden:
Commonly the gardener relies on stray seedlings, but one year he wakes up to see no seedlings at all. I enjoy saying I have none at all after about the third year, and I enjoy saying this because it suggests that I weed so carefully that no little self-sown seedling has a chance. It is far otherwise. I think the trouble is I have so many weeds that no self-sown seedling has breathing space.
By this definition I must be doing about the right amount of weeding because I often get self sown seedlings and the beds are not yet overrun with weeds.
I was really shocked a few years ago to see that I was getting self sown peonies. This is through absolutely no virtue of my own - they just appeared. I thought I was quite lucky and special until I mentioned it to Patrick Lima at Larkwhistle and he said, "Yeah, they do that now and then. They're always single reds"
Oh well. I can see by their distribution that they tend to appear under certain peonies but I'm never on top of things enough in June to keep track of which peonies are creating progeny. The only exception to this rule is one peony I have planted by itself. It is at least the MOTHER of the baby peonies appearing beneath it. There are lots of self-sown alliums in the picture below (at least most of it isn't grass), and you can see several tiny peonies.
You can see that one of the babies is going to bloom this year in this picture:
The parent is a Saunders hybrid called 'Lustrous'. You can often find interesesting peonies very reasonably at Wild's. I f you're willing to poke through catalogs and wait. I paid $9 each for 'Lustrous' and 'Rushlight' in 2002. They say you can contact them with specific requests but I never got an answer when I did.
You can read something about professor Saunders and the peonies he bred here.