Recent advances in inference techniques have opened new pathways for unveiling the hidden structures and dynamics of accretion disks. By integrating physical insight with modern statistical and machine learning tools, it is now possible to infer key properties of systems where direct observation is limited or impossible. This article surveys a series of studies illustrating this trend. First, we address ill-posed inverse problems, where sparse regularization enables the reconstruction of disk structures from indirect observables, ranging from power-spectrum estimations and Doppler tomograms to black hole shadow imaging. Second, we explore time-series analysis techniques based on state-space modeling, which separate spectral components in X-ray binaries. Third, we present dynamic mode decomposition applied to hydrodynamical simulations of accretion disks, revealing eccentric and m=3 modes associated with the disk reaching the 3:1 resonance. Fourth, we demonstrate an information-theoretic framework for autonomous observational decision-making, as implemented in real-time follow-up observations of cataclysmic variables with the Kanata telescope. These examples highlight how data-driven modeling can reveal unseen aspects of accretion phenomena across diverse astrophysical contexts and timescales.