Index to Marriage Record Sullivan County, Indiana Inclusive shows: Joseph Hiatt married Cynthia Thorn, 21 Sept 1870 (Bk.3,Pg.558)
1880 Cenus Gill Township, Sullivan County, Indiana 209/209
Hiatt, Joseph 36 w/m hus/marr/FL/d/d Oh Oh Oh Hiatt, Cintha A., w/f wife/KH/ In In In Hiatt, Charles F., w/m 8, son/AS/ In Oh In Hiatt, John D.S., w/m 4, son/ In Oh In Hiatt, Roy, w/m 1mon/b.May/son/ In Oh In
FL = Farm Labor d/d - deaf/dumb KH = Keeping House AS = Attending School
I could not find Joseph/Josiah Hiatt or Cynthia Thorn/Thom on the 1870 Census.There is a Joseph listed, but not right age or birth state for him to be yours.