Could you filter coffee back to being pure water? Okay, so coffee filters remove solid matter from the beverage, whilst leaving the remaining coffee intact for caffeiney goodness.
But it's got me thinking. Is there a way we could filter the coffee out of coffee, leaving water behind?
I know it could be done by distillation, collecting and cooling the steam, I'd also be interested in other approaches to turning coffee back to water.
 A: If you want to filter out the grains then certainly you could using normal filter papers in a filter funnel and repeat until the solution is clear of bits. You could also use a sintered glass filter. However, there will still be compounds from the coffee dissolved in the water and so a molecular sieve could be used and/or a chromatography column to separate these from the water. (You could try reverse osmosis if you really want to try an extreme method and have heaps of lab equipment and time). In practice it is probably easier just to distill the water off in the usual chemical lab way. Of course you could drink the coffee and inevitably separate out the water!
A: Coffee is a homogeneous solution hence it can not be separated by usual methods. 
I have few suggestions may not be very accurate but good for brainstorming. 


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*Distillation : Although you have mentioned not to mention it but I would like to add that coffee has several aromatic organic compounds that make the smell of coffee hence you can not get rid of them very easily by distillation (unless they evaporate completely during the process)

*Reverse Osmosis: This is your best bet, easiest by far. Problem is that the reverse osmosis may filter a very small amount (I dont know how small) of water out of coffee. Stronger the coffee lesser amount of water is filtered.

*Precipitation: you can mix certain precipitants to the mixture but now you have to worry how to remove the precipitant. 

*Ion Exchange: This is also a method to purify the water, It remove ionic salt from water however it will not affect covalent organic compounds. 

*Absorbent purifier: Several materials such as active charcoal can absorb impurities, I am not sure that charcoal may work or not but you can find some material that can absorb coffee from the water and term it 'coffeescopic' (inspired from hygroscopic).
You may also think of more exotic techniques like centrifuge as suggested by @Franklin, I am not familiar with molecular sieve or chromatography column so I can not comment on them. 
A: I'd think of effusion effect, centrifugal techniques or other methods used for uranium enrichment. You could possibly select particles with the right mass (mass of the water) out of this mixture in a lot of iterations. It would be long and very expensive but probably possible. 
A: In a sense, you can consider chromatography to be a kind of 'filter', and it can certainly separate out coffee components, including water.   There's no lack of other ways, though, to extract water.  Freeze drying would carry the water vapor
away, and you can sell the residue as instant coffee...  
