Grey dots appear where edges are very close to each other on an AO bake

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I’ve noticed these annoying texture baking artifacts that appear in areas where the edges from triangulated faces are very close to each other. This is just best explained by the images below. The first shows the problem, and the second shows the two edges that appear to be causing the problem, and this is further shown by the third image. I’m baking this on a 2048x2048 map with 1024 samples. Is there any way to fix this without changing the triangulated geometry?

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