Is cellulose soluble in water?

纖維素(cellulose) is insoluble in water. However, cellulose can lose its structural formation under high heat (but not dissolve) in contrast to starch, cellulose is also much more crystalline. Whereas starch undergoes a crystalline to amorphous transition at 60 -70 °C in water (as in cooking), cellulose requires 320 °C and 25 MPa to become amorphous in water. Its only soluble in acetic/nitric acid, and some part of sodium hydroxide.

In order to answer your question, I must classify cellulose into two domains: one is soluble fiber (cellulose) while the other is insoluble fiber (cellulose). For soluble one, it can be obtained from cell wall such as pectin. Besides, another one called amylose, a straight chain celluloses, is also soluble in water. These are typical celluloses soluble in water.
However, for those insoluble one comes directly from cell wall such as some found in vegetables which is branched cellulose consisting of both amylose and amylopectin. This branched cellulose consists of beta-glucoses formed by both 1,4 - and 1,6- formed glycosidic linkages making itself insoluble in water.
I hope you will find my writing helpful.