The 2xDSD digital signal at the output stage of the DAC has a certain noise floor. For simplicity of explanation, imagine that it’s 100dB lower than the maximum signal level the DAC can create in the audio band below 20kHz, but it rises through the octaves above that to be a whole lot of ultrasonic noise. (The actual noise floor is lower than -100dB, this is just an easy figure for illustration.)
The passive, analog low-pass filter stage is designed to let all the content below 20kHz pass through (both the desired audio and the noise floor) and then as the frequency rises impose greater and greater limitation on the unwanted ultrasonic noise so that a minimum amount of it reaches your amplifier.
The shape and level of that filtered noise is fixed. It doesn’t alter when you adjust the volume setting of the DAC. Even if you are playing no audio, that noise floor is still leaving the DAC and heading to your amplifier.
Now let’s imagine you have a piece of music which peaks all the way to the maximum digital signal level. If you have the DAC volume set to 100 and the attenuator off, the peaks of the music will be stretching the output of the DAC to its maximum level. Since we have a noise floor roughly 100dB lower than that, your signal-to-noise ratio there is 100dB. Awesome.
But your amplifier and speakers might take a signal at that level and produce a sound that’s way louder than what you want to hear. So you turn down the DAC volume control, way down to 20. Each volume step on the DS DAC is half a dB, so -80 volume steps is -40dB in signal level. But the noise floor hasn’t changed. Your signal now peaks at 40dB below maximum, and your noise is still there at 100dB below maximum, so your signal-to-noise ratio has dropped to 60dB.
If your amp and speakers are very sensitive, this can happen and the noise becomes intrusive in your listening experience. So, here comes the attenuator.
The attenuator takes the analog output of the DAC and throws some of it away. 20dB worth of it. Doesn’t discriminate between audio signal and noise. Everything gets 20dB quieter, including the noise. Reaching the same listening level requires you to turn the volume control up to 60 (adding 40 half-dB steps for an extra 20dB of signal) but your noise doesn’t get any higher. So now you are listening to the same signal but with the noise 20dB lower. You now have a signal-to-noise ratio of 80dB instead of 60dB.
This increase in SNR at the same volume only applies if you normally listen with at least 20dB of unused headroom – ie with your volume set to 60 or lower, meaning you are able to increase to 100 after enabling the attenuator.