Higher concentration of certain dissolved gas in subsurface will diffuse into the surface layer with lower concentration of this dissolve gases via eddy diffusion, if the stratification is strong and the gradient of dissolve concentrtion presents between these two layers. Assuming that there is a layer of cold winter water in the polar ocean, contains higher concentration of the dissolved gas than that of below layer but undersaturated with this gas, whereas the below layer is oversaturated with the gas, but with lower gas concentration then what will the direction of eddy diffusion be? from the undersatruated, higher dissolved gas concentration cold water to the oversaturated, lower dissolve gas concentration warm water or on other way round.
According to Fick's first law the diffusion is directed from high to low concentration (unless one allows for negative diffusivity). The second relevant law is the one from Henry, stating that the saturation concentration is proportional to the pressure exerted by a gas on a water body. That means the saturation concentration in the warm water will increase thus allowing the diffusion from the cold water with higher gas concentration to the warm water with the lower one.
If you wanted to think about it in terms of thermodynamics, the gas will diffuse from regions of higher chemical potential (higher activity in the thermodynamic sense) to lower chemical potential (lower thermodynamic activity). So if the activity coefficient of the gas increased with temperature, that might compensate for the lower concentration. If there was some pathologic gas whose activity coefficient was highly temperature dependent, or adjusted some other water property (maybe ionic strength) to get a strong activity gradient across the temperature boundary, you could get diffusion from lower concentration (high activity driven by temperature (or ionic strength)) to the higher concentration (low activity driven by temperature (or ionic strength)). I'm not sure such a gas exists, but in principle it is possible. I think.
However, in general, at Peter said, in cases where the activity coefficient is constant (relatively) diffusion goes from regions of high concentration (high activity) to lower concentration (lower activity).
Also, keep in mind that in your example, heat diffuses about 100 times faster through water than a gas (ratio of the Prandtl number to a typical Schmidt number of 1000 for a gas (e.g., Sc for CO2 at 20 C in seawater is around 666)), so that temperature equilibrates faster through diffusion than the gas. Therefore the gas concentration will be diffusing through an isothermal concentration boundary layer and the saturation pressure will follow the gas concentration.
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