Transient electromagnetic (TEM) logging can reflect the electrical properties of formation around the borehole in the time domain, serving as an important method for detecting oil and gas reservoirs, coal seams, groundwater and geothermal resources. However, conventional optimization inversions suffer from high computational costs and poor convergence stability, while supervised deep learning methods rely heavily on high-quality training datasets, limiting their applicability in complex geological environments. To address these challenges, this study proposes an unsupervised time-domain inversion framework based on physical–prior constraints. The framework integrates a finite-volume time-domain (FVTD) method with the adjoint-state method to enforce Maxwell's governing equations during optimization. We construct a generative network that combines convolutional neural network (CNN) with Transformer, achieving an effective fusion of local structure characterization and long-range dependencies. Moreover, a dynamic weighting strategy incorporating geological prior balances data misfit and prior constraint terms to constrain the solution space. Numerical experiments demonstrate that the proposed method achieves excellent imaging accuracy and stability across near-borehole, deep, cross-scale, and radial dual-anomaly scenarios without requiring any training dataset, significantly enhancing the reliability of TEM logging inversion.