Ok I am currently setting the code P1451 and running regens constantly. I am rolling white smoke out while in regen. I had put around 6000 miles on the DPF delete kit from HS Performance. Yes, I have all sims installed, with the pressure box, and running a edge with attitude. From everything I have read this code is coming up from timers in the programing of the dpf software. I have emailed HS about this problem and I am currently waiting on a reply. I have also read that the XRT downloader they sell will allow you to turn off the DPF filter. What I am upset with is I was sold a kit that was promised not to have a regen cycle. They still currently show on their website that this kit will not regen. If I am instructed I can buy an XRT or take my truck to the dealer to clear the code. Taking it to the dealer sounds like it will be a fix for about 6000 miles or until the timers go off again. I think HS needs to be selling the XRT at a very reduced rate. I am curious to know what you guys that have had this problem found to be the fix in the end.
I had the same issue a while back...delete kit combined with an Edge w/Attidue. Truck ran great for a while (3000km) then went into constant regen...lots of white smoke. It would come out for a few seconds and then right back into a new regen cycle. Drove me nuts.

In working through the issue with the techs that sold it / installed it...we determined that it was an issue between the Edge electronics & the DPF delete electronics...they just don't work well together, particularly with the Attitude. Apparently it's not an uncommon issue. My understanding is that the Edge w/Attitude is made to work primarily in trucks with a DPF.
Fortunately, the shop that sold me my stuff returned it all and exchanged it for the XRT kit. Since then, not a single issue, and the truck runs WAY better than it ever did with the Edge!

If it's not an option then definitely follow James (RSD) and MATTIAC's advise a...check the sims for moisture and swap them out for 330s. You probably should do that asap regardless...stop running crappy air through your engine until you resolve the main issue (Edge w/A + most DPF electronics / sims = constant regen).
Good luck!