Ive seen commercial sound-absorption panels that are like a kind of open-cell styrofoam, with holes drilled into them at regular intervals of a couple of inches. The places that sell this stuff also sell softer "eggcrate" type foam material. It is my understanding that the "eggcrate" stuff absorbs higher frequencies, and the harder foam stuff behind it (which is itself 2-3" thick) absorbs mid-to-lower frequencies.
You could make diy panels out of regular styrofoam packing materials. Make them irregular with plenty of variable depth, so sound waves will deflect and reflect around and stand a greater chance of being absorbed. Drill (melt, probably) some holes into it, too, for further absorption. What isn't absorbed will be diffracted, not a bad thing for audio. You could put something like pillow batting in front of it, held in by a wooden frame covered with chicken wire and with grill cloth (or fairly permeable decorative cloth) over that. It should look good and work well.
Depending on the amount of absorption (versus reflection and diffraction) you want, you could use decorative picture-framing strips around the frame edges, a more decorative cloth, and perhaps even some decorative elements set onto the cloth. Acoustic panels like this can even be set behind pierced fretwork carvings, paintings or beautiful woodgrain panels, making them look like an integral part of the room decoration/design. These things will, of course, increase reflection and/or diffraction, and decrease absorption. But sometimes not as much as you'd think, because the decorative elements in front will also "bounce" the waves that come in from the sides (and around them), helping to further dissipate/absorb them.
