Seth Killian answered some concerns about Marvel vs Capcom 3 on Capcom-Unity's Ask Capcom forums today. Some users were concerned that there might be no VS CPU option available.
"Just to cut to the chase here, you can indeed play against the CPU to your heart's content. Against any teams, at any difficult, and even on any stage you choose.
It's not pulled out as a separate "mode," but it's easily done in training mode. You pick the dummy team, and then all you need to do is set the training dummy to "CPU" and turn life recovery to "OFF." You can select the difficulty, and just go at it. It's great for practicing against certain teams, and the CPU at the hardest difficulty is, umm, actually hard.
When the CPU (or you) has been killed off, the match just immediately restarts from the beginning. You can change characters whenever you want, or change assists from the menus without even going back to the character select screen.
The training mode in this game is extremely, extremely good. From the easy record and replay functionality to practice against certain setups, to the huge variety of customizable dummy options, I think it's the best we've ever done. Hope this answers some questions."
On top of this, rumors have been swirling around today that the training mode lacks a Record/Replay function. Seth has said in no less than four interviews now, including this one, that training mode does allow Record/Replay, so lets put this rumor to rest.