I have a craftsman riding mower with a 16 hourse B& G engine.
I have cleaned and rebuilt the carb with the proper kit,
Put in new diaphram (before it wouldn't start at all) and soaked and cleaned the carb.

Now it cranks great and will run (though not well enough to mow) with the choke completely closed. If I try to open the choke it immediately dies. I am fairly handy with mechanical stuff, but not an expert. What else am I missing.

Could it be the fuel pump?

It has a diaphram in the carb to pull fuel. I replaced the diaphram (I think correctly) when I did the rebuild and cleaning.--- It may be possible that something slipped when I put it back together but it is pumping