I once poured some diesel fuel into a small container, struck a match and touched it to the diesel fuel. The match went out.
Diesel fuel doesn't burn except under special conditions, and unlike gasoline it doesn't form an explosive vapor. That's why it, and the heavier fuel oils are the preferred fuel for ships and why diesel was preferred for submarines before nuclear power. So long as you store your fuel outside, and observe the usual precaustions such as not leaving oily rags hanging around and contain any spills, you shouldn't have a problem.
Diesel won't start a fire, but if it's heated sufficiently, like in a burning rag, it will burn. As has been mentioned, veggie oil is probably even safer than diesel.
If you're running your engine in your basement you have a LOT of things to think about, and fire is a ways down the list. This topic was explored some time ago. Fire and building codes are often annoying and seem arbitrary, but if ANYTHING should happen as the result of your running an engine inside your home, your insurance will not cover you and you expose yourself to civil and criminal liability.
Quinn