Welding occurs during transport and deposition of volcanic particles in diverse settings, including pyroclastic density currents, volcanic conduits, and jet engines. Welding rate influences hazard-relevant processes, and is sensitive to water concentration in the melt. We characterize welding of fragments of crystal-free, water-supersaturated rhyolitic glass at high temperature using in-situ synchrotron-source X-ray tomography. Continuous measurement of evolving porosity and pore-space geometry reveals that porosity decays to a percolation threshold of 1–3 vol.%, at which bubbles become isolated and welding ceases. We develop a new mathematical model for this process that combines sintering and water diffusion, which fits experimental data without requiring empirically-adjusted parameters. A key advance is that the model is valid for systems in which welding is driven by confining pressure, surface tension, or a combination of the two. We use the model to constrain welding timescales in a wide range of volcanic settings. We find that volcanic systems span the regime divide between capillary welding in which surface tension is important, and pressure welding in which confining pressure is important. Our model predicts that welding timescales in nature span seconds to years and that this is dominantly dependent on the particle viscosity or the evolution of this viscosity during particle degassing. We provide user-friendly tools, written in Python™ and in Excel®, to solve for the evolution of porosity and dissolved water concentration during welding for user-defined initial conditions.