FDA approved permanent fillers for buttocks ?

It is very difficult to determine the exact size and shape implant you will require to best match your ideal butt image without an examination by a board certified plastic surgeon. Not just any board certified plastic surgeon, but one with many years of frequently performing breast augmentation surgery including different approaches, techniques and implant choices. This is because several measurements not to mention your breast characteristics are needed to determine the optimal implant size to obtain your goals. Without knowing these dimensions it would be difficult to make this determination. For example, the existing base width of your buttock will determine, in many cases, the maximal volume per implant profile that you can accommodate. Liposuction of your lower back and fat transfer is also helpful as an adjunct to implants. Using “want to be” photos however are useful if simply provided to the surgeon.

There currently is NO FDA approved injectable filler for buttock augmentation.
 I actually practice here in Los Angeles and I have unfortunately had many patients come to me after having their high hopes for buttock/hip augmentation crushed by measly Sculptra (what Dr. Ourion uses) results or other "fillers". Critical points of awareness are: 1) Sculptra is temporary, it will last 1.5 - 2 years at most, 2) if done correctly, and with  real not fake, dermal fillers like Sculptra are cost prohibitive for 99% of potential buttock augmentation patients. In order to create a significant/noticeable result with a dermal filler, at least 200 mls of product must be injected into each buttock cheek for a total of 400 mls. At $1000 per ml, this equates to a minimum price of $400,000.00. Thus if your doctor is recommending to put in ONLY 20 or 40 mls of sculpture you will pay $20,000-$40,000 and get an insignificant miniscule result!...like putting a "drop of water in the ocean". 3) Do not let anybody tell you that the product is so special that it's going to magically grow over the following months or years...this just does not happen to any noticeable degree!, 4) dermal fillers, when injected in large quantities, have a relatively high infection rate, guaranteed tendency to migrate away from the original area they were injected into, and almost always stimulate a lot of inflammation with a subsequent and disastrous amount of scar tissue/hardening, and 5) the one very serious complication that can rarely (< 1%) happen is "embolism" in which the filler gets into the blood stream and travels up into the lungs, heart, and/or brain causing serious problems, including death. 
 On the other hand, buttock/hip implants are actually a very good, safe, and permanent reliable option for most patients seeking buttock/hip augmentation.  Contrary to nieve claims by many other plastic surgeons, intended to scare patients away from implants, my overall complication rate is only ~5%.