No, there is no connection (not bond) between these two words except that they are spelled similarly. But there are other ways to say it too. You can say, "does anyone know if there are any similarities between these two words?"

Look at the Word Origin sections (there is a handy map and an explanation below it): http://dictionary.reference.com/browse/improve http://dictionary.reference.com/browse/improvise It seems there is nothing in common based on word origin...

"improve" means to make something better. "improvise" means to use something that was not intended for the purpose. I must improve my Japanese language skills. I don't have a tool to make the necessary repairs, so I'll have to improvise.