Final render different from viewport preview

I have recently run into an interesting problem. When I render a certain object in the rendered viewport (200 samples), it renders with a very soft edge, which I want. However, without changing anything, when I give it a final render (F12 render, 500 samples), the edge becomes very hard. Why are the two different, and how can I achieve the soft edge that I want in the final render?

Here are some images explaining what I mean:

Rendered Viewport (soft edge):

Final Render (hard edge):