Whooshing noise when not accelerating

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2014 Audi A6 2.0T w/ 38000mi
Any thoughts on what might be causing a whooshing noise at times when the car is not accelerating? I do not hear the noise when the car is stopped, which suggested some kind of issue with the pads or rotors, but the noises present even when not applying the brakes. In fact, braking does not increase or decrease the noise, but it goes away immediately upon applying the gas.

Does the car operate normally in all other respects? Did this noise start gradually or suddenly?

The car does operate normally otherwise. I can’t say for certain whether it gradually became noticeable or happened suddenly, but I can’t pin the start of the noise to a particular event such as new tires, brakes, a particular service, or some other event.

When you press on the gas pedal, the intake manifold vacuum is immediately greatly reduced. So any device which uses or is otherwise connected to that vacuum source could be the cause.

Power brake booster, fuel tank evap venting & purge valves, egr, pcv, etc.