Flattening folder structure

I have this folder structure:

├── foo1
│   ├── bar1.txt
│   └── bar2.txt
├── foo2
│   ├── bar3.txt
│   └── bar4 with a space.txt
└── foo3
    └── qux1
        ├── bar5.txt
        └── bar6.txt

that I would like to flatten into this, with an underscore between each folder level:

├── foo1_bar1.txt
├── foo1_bar2.txt
├── foo2_bar3.txt
├── foo2_bar4 with a space.txt
├── foo3_qux1.bar6.txt
└── foo3_qux1_bar5.txt

I've looked around and I haven't found any solution that work, mostly I think because my problem has two particularities: there might be more than one folder level inside the root one and also because some files might have spaces.

Any idea how to accomplish this in bash? Thanks!

Edit: Running gleen jackman proposed answer I get this:

There are two underscores for the first level folder. Any idea how to either avoid this or just rename it so that is just one underscore? Thanks.