You don't need a massive amount of energy. We could be launching interstellar probes now with current technology. They'll just take 10s/100s of thousands of years to get anywhere.
The real problems are political, technological and ecological stability.
No one has ever built electronics capable of lasting hundreds of thousands of years. It's not obvious if it's possible because on those timescales everything crumbles to dust, especially if it's constantly being abraded by dust and radiation.
And if you don't put your travellers into long-term suspension, political and cultural stability are even more fragile.
And small eco-systems are far less resilient than planet-sized systems - which, it turns out, may not be resilient at all on longer timescales.
So the gap between launching Voyager I/II and launching a self-replicating probe which can reproduce itself physically and culturally is beyond huge.
If you happen to have massive amounts of energy some of these problems get easier, because you can get where you're going more quickly. But some remain immensely difficult.
Which is why percolation is a much better model. There will inevitably be some attrition in any colonisation program, and there may well be a hard limit on the amount of entropy any colonisation program can survive.