Source localization has been widely studied in recent years due to its crucial role in controlling the spread of harmful information. Existing methods only achieve satisfactory performance within a specific propagation model, which restricts their applicability and generalizability across different scenarios. To address this, we propose a Generalized Diffusion Framework for Source Localization (GDFSL), which enhances probabilistic diffusion models to flexibly capture the underlying dynamics of various propagation scenarios. By redefining the forward diffusion process, GDFSL ensures convergence to a real distribution of infected states that accurately represents the targeted dynamics, enabling the model to learn unbiased noise in a self-supervised manner that encodes fine-grained propagation characteristics. A closed-form reverse diffusion process is then derived to trace the propagation back to the source. The process does not rely on an explicit source label term, facilitating direct inference of sources from observed data. Experimental results show that GDFSL outperforms SOTA methods in various propagation models, particularly in scenarios where historical training data is limited or unavailable. The code is available at https://github.com/cgao-comp/GDFSL.