There is no one great treatment for acne scars. Each has its advantages and disadvantages. I usually recommend the combination of several different treatments Fat grafting may help by several methods. Just placing the fat may be a subcision method of undermining the depressed scars. It will be more helpful for saucer scars than icepick scars. The fat may give a "stem cell" like effect with improvement of the complexion. I usually use Juvederm as I can place it more superficially than fat. We use the microneedling as well. It creates more collagen and plumps the area. It is a series of treatments, but recovery is minimal and costs are low. We sometimes use a non invasive laser such as Cool Touch or Thermage for tightening. We do subcision of areas. We also will excise small icepick scars. We rarely recommend invasive lasers, as the results are limited for such a long recovery and risk.
There are different types of acne scars and many of them are very difficult to improve. Generally saucer-shaped or box acne scars respond best to filler injections as it needs a widely-based acne scar to allow it to be pushed outward. I would test the 'underneath' approach by having a synthetic filler placed first to test the concept. If successful you may then undergo fat injections possibly combined with laser resurfacing on the outside at the same time.