"the idea started simple" vs "the idea started simply"

What is the difference in meaning between the two phrases in the title, and are both gamatically correct?

My impression is the following:

1. "The idea started simple" = In the beginning the idea was simple.

2. "The idea started simply" = It was easy to get the idea started.

Then there is also the following:

3. "The idea simply started" = the idea started spontaneously.

Are my impressions correct?