It seems NVIDIA have been working on some improvements to their Linux driver, as the 396.54.05 beta driver seems to have improved performance in various games.
Tweeting about it, Valve's Pierre-Loup Griffais said "Proton NVIDIA users: the latest 396.54.05 Vulkan Beta driver contains significant performance improvements in GPU-bound scenarios.". He also noted that those on Ubuntu can grab it from a different PPA provided by Canonical for easy installation.
Looking around, it seems he's right on the money. Talking about it in our forum (also reddit), users noted improvements to games run on Linux. The improvements look pretty impressive too. The focus of everyone's testing seems to be DXVK which benefits from the new driver, so I went to test.
I was going to try out DOOM this morning, to see if there were any improvements there myself, but sadly the latest Proton update has actually made it unplayable for me when using two monitors (issue report). A shame, because it was basically perfection on the initial release of Proton from Valve's Steam Play. A good case for not simply moving everyone onto the latest version, keeping older versions around for when they do work fine. Edit: As mentioned in our comments, DOOM is not a good test case anyway, I simply don't own enough Windows games currently to test such stuff, but I'm working on acquiring more for such testing.
Instead, I took a look at Rise of the Tomb Raider and F1 2017 two native Linux games with Vulkan but it gave practically no difference. Edit: As mentioned by the DXVK developer in our first comments, the driver update will mainly benefit DXVK (for now) anyway.
So for those of you who are playing games (when they work) with Steam Play, this driver should hopefully improve things for you.