Pyroclastic flows produced by large volcanic eruptions commonly densify after emplacement. Processes of gas escape, compaction, and welding in pyroclastic-flow deposits are controlled by the physical and thermal properties of constituent material. Through measurements of matrix porosity, permeability, and electrical conductivity, we provide a framework for understanding the evolution of pore structure during these processes. Using data from the Shevlin Park Tuff in central Oregon, United States, and from the literature, we find that over a porosity range of 0%–70%, matrix permeability varies by almost 10 orders of magnitude (from 10^–20 to 10^–11 m²), with over three orders of magnitude variation at any given porosity. Part of the variation at a given porosity is due to permeability anisotropy, where oriented core samples indicate higher permeabilities parallel to foliation (horizontally) than perpendicular to foliation (vertically). This suggests that pore space is flattened during compaction, creating anisotropic crack-like networks, a geometry that is supported by electrical conductivity measurements. We find that the power law equation: k₁ = 1.3 × 10^–21 × ϕ^5.2 provides the best approximation of dominant horizontal gas loss, where k₁ = permeability, and ϕ = porosity. Application of Kozeny-Carman fluid-flow approximations suggests that permeability in the Shevlin Park Tuff is controlled by crack- or disk-like pore apertures with minimum widths of 0.3 and 7.5 μm. We find that matrix permeability limits compaction over short times, but deformation is then controlled by competition among cooling, compaction, water resorption, and permeable gas escape. These competing processes control the potential for development of overpressure (and secondary explosions) and the degree of welding in the deposit, processes that are applicable to viscous densification of volcanic deposits in general. Further, the general relationships among porosity, permeability, and pore geometry are relevant for flow of any fluid through an ignimbritic host.