Diffie-Hellman is only a key exchange protocol and does not provide forward secrecy. Imagine that my and your client figure out our shared secred (key) with DH, then encrypt our chat with that. If someone breaks only a bit of our traffic, then they can read newer messages as well.
Forward secrecy means that at any point messages are encrypted with keys that aren’t reused forever, which means if an attacker can intercept traffic and read a bit, or crack the encryption, that they don’t automatically get access to our future conversation as well.