<p>Three-dimensional quantitative phase imaging has been extensively studied in X-ray microtomography to improve the sensitivity and specificity of measurements, especially for low atomic number materials. However, obtaining quantitative phase images typically requires additional measurements or assumptions, which significantly limit the practical applicability. Here, we present preconditioned Wirtinger flow (PWF) to realize an assumption-free, single-shot, quantitative X-ray microtomography. Accurate phase retrieval is demonstrated using a specialized gradient-based algorithm with an accurate physical model. Partial coherence of the source is taken into account, extending the potential applications to bench-top sources. Improved accuracy and spatial resolution over conventional speckle tracking methods are experimentally demonstrated. The various samples are explored to demonstrate the robustness and versatility of PWF.</p>