How to connect 24" Apple Display to HDMI output of Mac Mini 2011?
Unfortunately, adapters like that don't exist, AFAIK.

That is, you can't just convert from HDMI to DisplayPort via a simple cable. The [Mini] DisplayPort to HDMI adapters aren't just cables, they contain IC's that provide an HDMI interface. I don't know of any such adapter that works in the other direction.