Diddy 's lawyers are painting him as a loving father and pillar of the community during his sentencing ... and, we've got the video they plan to use to get that message across.

The defense released a nearly 12-minute-long vid they already submitted to the court ... which begins by showing Diddy sitting with his kids -- speaking softly to his twin daughters, D'Lila and Jessie .

The rapper plays with a paper puppet and sits on the floor while his kiddos try to steal his sunglasses ... looking every bit the attentive father.

The video shifts to his good work in the community ... including events where he's opening schools, speaking to graduating classes and handing out a huge check to some eager students. Gallery Launch Gallery Getty

Kim Porter 's passing is included in the

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