Meaning: Abundant or plentiful
* She offered profuse apologies for her mistake. (She apologized a lot.)
* The garden was filled with profuse blooms of roses and lilies. (There were many flowers.)
* He expressed his gratitude with profuse thanks. (He thanked her many times.)
* The artist used profuse colors in her painting. (She used many colors.)
* After the heavy rain, the river flowed with profuse water. (There was a lot of water in the river.)
Meaning: Excessively abundant
* The wound was bleeding profusely. (The blood was flowing out heavily.)
* He sweated profusely as he climbed the mountain. (He was sweating a lot.)
* The restaurant offers a profuse menu with many options. (The menu has many choices.)
* The book contained profuse descriptions of the characters. (The book described the characters in great detail.)
* She received profuse compliments on her new dress. (She received a lot of compliments.)
Other examples:
* The tree's branches were covered in profuse foliage.
* His profuse knowledge of history was impressive.
* The wedding was a lavish affair with profuse decorations.
Remember that "profuse" usually implies something positive, like abundance or generosity, but it can also be used to describe something negative, like excessive bleeding or sweating. The context will usually make the meaning clear.