The truth is there is no such thing as differential mode noise and common mode noise. All radiation is dependent on the energy of the field between two points and every source of noise is dependent on a difference in electrical potential between two points.
Now with your differential signal there is a potential difference between the positive and negative terminal. Relative to earth ground the energy source, for instance a battery, has a higher potential as well. Even if earth ground and a battery are not connected there is a parasitic capacitance between them that depends on their distance and the geometry of the conducting plates. Usually this capacitance is in the range of picofarads.
There is always a current loop when there is a difference in potential, and E and M fields exist infinitely in space. The gradient of an E field is a potential difference and parasitic capacitances have a current known as displacement current. A very small current usually but it can be large given the right circumstances.
Therefore there is a path for all of your currents on your board that goes through ground and returns to your battery. Typically these are decomposed into a common mode current representation but it's equally fine to see them just as the capacitively coupled path to earth for this particular potential difference.
So what are we doing when we add a capacitor from our circuit to earth? We are doing the exact same thing when we add a decoupling capacitor in our differential line, changing the impedance of the path for different frequencies. If we have a 1m wire whose capacitive coupling is equal along the length we get a particular frequency response for the signal. If we add a capacitor the frequency response changes because we introduce at a particular point a lower impedance path for certain frequencies. This will depend on where along the length of the line we place the capacitor and the value of the capacitance. We influence both the loop area, and the impedance.
To most effectively do this, which is fundamentally just manipulating the cut off frequency for a low pass LC filter, we need to make the decoupling to earth equal for both lines. This minimizes the noise between a line and earth without adding differential noise.
In fact one can completely remove common mode signals in a circuit through a method known as impedance balancing, akin to an impedance balanced bridge.
If the impedance in a bridge is balanced the currents through the center path is nullified. If you consider the battery in this image to be earth injecting a common mode current into your circuit, take point 1 as V+ and point 2 as V- of a DC source, you can effectively use this to remove common mode currents from your circuit and hence common mode noise entirely (theoretically of course).
The above shows radiated emissions with both differential and common mode noise so it's not entirely clear how effective this is for the lower frequencies, but you can also get a greater reduction in common mode noise if you attempt to decouple to earth at the load.
Here the peak line is shown for radiated emissions of only the common mode noise. This method also decouples to earth at the load and is quite significant in its reduction.
Note: You may need to watch out for leakage current to earth through your capacitors depending on the voltage of your application in terms of safety standards.
Modelling and measurement of high frequency conducted electromagnetic interference in DC–DC converters - Grobler, Gitau
Modeling and Optimization of Impedance Balancing Technique for Common Mode Noise Attenuation in DC-DC Boost Converters - Zhang, Zhang, Lin, Takegami, Shoyama, Dousoky
A Study on Common-Mode Noise Generation in Switching Circuit due to Unbalanced Characteristic - Intachot, Klungwijit, Prempraneerach, S. Nitta