I suspect the problem is from an incorrect error margin value for the depth of field shader pass (which probably is also tied into the Ambient Occlusion pass)
I was able to fix it myself and for several of my friends by editing these values in my Fallout4Prefs.ini and setting the INI file to read-only.
[Display]sAntiAliasing=TAAiShadowMapResolution=2048iVolumetricLightingQuality=2bVolumetricLightingEnable=1[Imagespace]bDoDepthOfField=1bScreenSpaceBokeh=1bMBEnable=0bLensFlare=1[LightingShader]bScreenSpaceSubsurfaceScattering=0bScreenSpaceReflections=1[BlurShaderHDR]bDoHighDynamicRange=0[BlurShader]bUseBlurShader=0
If it still persists, try to change the "bDoDepthOfField=1" to equal 0 instead.
Good luck, let us know how this 'fix' goes for you!