Or, we could do some simple back of the envelope mathematics in the present.
Okay, what is the concentration of carbon in seawater? It is 28 parts per million, so to make just one liter of diesel ( between 8 and 21 carbon atoms per molecule), I need to process between 285,000 to 714,300 liters of water (assuming 100% extraction efficiency-good luck with that). In gallons, I need to process roughly 70,000-180,000 gallons of seawater to get the carbon for one liter of diesel fuel. How much energy is needed to pump roughly 120,000 gallons through the processing system for that carbon to make up that one liter? And that is the energy needed just to supply the raw carbon. Additional energy is needed to then recombine the carbon and hydrogen into diesel. Remember, the First Law of Thermodynamics means you need to put more energy into making the diesel fuel than you will ever get out of it.
If I assume I need roughly 100,000 gallons (a WWII diesel sub load) of fuel, then I need to process (at 100% efficiency) 48000000000 gallons of sea water just to obtain the carbon I need. And, a gallon of seawater weighs just over 8 Lbs., so you need to process 192,000,000 tons of water just to get your carbon. Then I need the additional energy to make the diesel from hydrogen and carbon. Oh. yeah, and you need energy to extract the hydrogen from water as well. Better bring one hell of a very large nuclear reactor to power the whole process.