Compositing woes

Using NVidia’s Vulcan demo as inspiration, I decided to use a smaller render texture to cut down on my smoke and fire fillrate, and composite over my scene.

It does wonders for peformance, but the artifacts are pretty bad.

Here’s a screenshot:

The fire won’t be blended this way in the final product, but the smoke will be. Any pointers on how to get rid of the aliased edges? Should I be blurring the low-res composite texture, blurring the final composite, or doing something else entirely?