Nice impressions. Maybe I am not understanding what is meant by "diffusion" in a technical sense. The HD800 has huge soundstage yet no shortage of details. is HD800 not diffuse. Can you have big soundstage a la HD800 without diffusion. Or does HD800 simply have some other magic going on to counter adverse effects of diffusion as you describe them.
Personally, I describe diffusion as a lack of coherency to the sound. As you pointed out, the HD800 has a very large stage with lots of low-level resolving capability, but it also sounds diffuse. The K812 was the same for me, though minus the resolving capability (piece of shit) and a slightly less realistic transition from the width to the depth. Lets look at the construction of both headphones, as they have a few things in common.

The HD800 has a metal mesh surrounding the driver inside the earcup. It also has foam insert/dust covers inside the cup.

The K812 also has metal mesh surrounding the driver, but no inserts. However, it also has a metal mesh directly
covering the diaphragm; this is not true with the HD800, which simply has a silk screen to protect the diaphragm.
Here's what I suspect. As pointed out, both of these headphones have metal mesh surrounding the driver to resonate with.
As we know thanks to Marv, the HD800 uses this to boost bass response, and I wouldn't be surprised if the K812 does the same. Unfortunately, doing this often incurs nasty side effects. When a specific frequency range begins to linger more than everything else, you start losing the sense of "togetherness" and coherency to the presentation due to certain timing information being lost in the haze. Measurements of the
K812 and
stock HD800 on this site show enough ringing to cause this.
Both headphones also have something between the driver and the listener's ear: The dust covers on the HD800 and the metal mesh over the K812's driver. This breaks up or "diffuses" the frontwave of the driver and in the K812's case, also serves as a type of dampening for the diaphragm. By the time the soundfront reaches your ear, it's been through materials which are not acoustically transparent (some to a greater degree than others), the result being a discombobulated wave of frequencies hitting your ears all at different times. This alters the timing of certain spatial cues in the recording and will make it more difficult to place an instrument in the soundscape. This factor is more in play on the K812 than the HD800, though, which is why the HD800 can sound better when the ringing caused by the metal mesh is quelled. The K812 might have similar potential, but removing the mesh will alter the dampening of the diaphragm, and will probably ruin the K812's good upper and lower range extension.
Just my 2 cents.