The only way I can construct a sentence in which 'to know different' is understandable to me is if there is a deep construction in which the word 'something' [something] is understood:

Example: John earnestly wished he could go to the game. If anyone knows [something] different, please tell us before we buy him a surprise ticket.

The construction above sounds casual rather than formal, but I can see how that use of 'different' with 'knows' would be understood.

I myself would write all of the above, but with 'differently' simply because the adverbial form feels more natural to my ear. In other words, I expect to hear '-ly' in that construction.