Where does the mass come from when you grow plants in water?
Short answer
Plants with storage compartments can grow for extended periods on water alone.

Background
It indeed seems the question is indeed different from the suspected dupe after all. 

According to Turesson (2014)


  Seeds, tubers and roots are the most common sites for [...] energy storage and the forms in which energy is stored are predominantly oil, starch and sugars. Underground storage organs mainly store starch and sugars, while seeds from different plant varieties accumulate high levels of starch and also oils and proteins.


So storage compounds like "seeds, tubers and roots" can sustain prolonged growth in the absence of pretty much anything, except water; just consider the familiar seedlings of cress on cotton wool (Fig. 1). There's basically nothing there, just water.


Fig. 1. Cress grown on cotton wool and water. source:Dreamstime

Reference
 - Turesson,  Carbon Allocation in Underground Storage Organs, Doctoral Doctoral Thesis (2014), Swedish University of Agricultural Sciences
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