Porous structures are made from compositions that include hollow glass bodies and an inorganic powder. The inorganic powder may act as a rigid frame member, a crystallization agent, or both, which reduces the shrinkage of the porous structures during firing. The porous structures made therefrom have an open porosity of greater than 70% and reduced shrinkage of less than 10% compared to the green structures prior to firing. Methods for firing the green structures made from the compositions are also disclosed, the firing methods including reducing a temperature ramping rate of the green structures during a crystallization temperature range of the glass of the hollow bodies.