Most likely common mode noise.
Whereas for differential noise, you have the right idea (shunt it with a cap, or make an LC filter), it doesn't do anything for common mode.
Rotate your perspective a little. Suppose the output DC+/- act, together, in parallel, as a single conductor (which is true, at RF, because there's a huge capacitor between them!). Suppose the mains AC H/N behave the same way (for the same reason, usually). Finally, suppose there were a noise source wired between these two connections.
In reality, there are four wires, but it doesn't matter which ones the noise source connects between, because each pair acts the same way at RF.
That noise voltage has to go somewhere. If mains is ultimately near or at ground, then the noise stacks on top, and your circuit is riding on the noise voltage.
When the noise voltage enters a sensitive circuit, you see interference problems. The hallmark of common mode noise is that it's "noise that's not really there", i.e., the circuit (for the most part) keeps on working as it normally does, yet you measure the same noise waveform /anywhere/ in the circuit.
The most illustrative method being: with an oscilloscope and 10x probe, clip the ground clip to the probe tip. Poke the tip into circuit 'GND' (which, because it's being driven by a noise source, is not really "ground", as the oscilloscope sees it!). Note the waveform is not actually zero, despite the probe tip being "shorted" by the ground clip!
Ground clips make very poor RF grounds, and the RF voltage dropped across that ~10cm piece of wire is what you measure.
What to do? Do the same thing as ever: filter it! You use an LC filter exactly the same way as usual: the prime difference is, you can't simply tie a huge capacitor from output to mains. You must use smaller (~1000pF) Y1 rated capacitors, which will withstand hazardous mains voltages without letting through much leakage current.
Since you're filtering pairs of wires, that ultimately aren't identical (they're carrying a DC or low frequency AC voltage, which is the whole point!), you can't simply use one inductor; instead, you use a common mode choke.
If the DC output should be isolated, you should use Y1 type capacitors (as small as practical), from AC H/N to safety GND, and from GND to DC output. If the output doesn't need to be isolated, simply ground it, so you need only the mains Y1 caps.
The ultimate purpose is to make the mains wires, and the output wires, have the same RF voltage: zero. The power supply is allowed to generate its noise voltage, which is dropped across a common mode choke. (The choke can be on either side of the power supply, but it's usually on the primary side because it can be physically smaller.)
Tim