Since DBE takes away part of the "signal", but not the noise, the signal to noise ratio decreases. Noise is usually quite easy to reduce by using TGVDenoise or MMT/MLT with noise reduction set for various layers. Personally for small scale noise in luminance, I prefer to use TGVDenoise in Lab mode on just L. For chrominance noise in DSLR images, I use MMT on about 7 layers with chrominance (restore CIE Y) as target. Quite heavy on the lower number layers, and decreasing in strength on the higher number layers.
Hope this helps,