Sparse-View CT (SVCT) reconstruction enhances temporal resolution and reduces radiation dose, yet its clinical use is hindered by artifacts due to view reduction and domain shifts from scanner, protocol, or anatomical variations, leading to performance degradation in out-of-distribution (OOD) scenarios. In this work, we propose a Cross-Distribution Diffusion Priors-Driven Iterative Reconstruction (CDPIR) framework to tackle the OOD problem in SVCT. CDPIR integrates cross-distribution diffusion priors, derived from a Scalable Interpolant Transformer (SiT), with model-based iterative reconstruction methods. Specifically, we train a SiT backbone, an extension of the Diffusion Transformer (DiT) architecture, to establish a unified stochastic interpolant framework, leveraging Classifier-Free Guidance (CFG) across multiple datasets. By randomly dropping the conditioning with a null embedding during training, the model learns both domain-specific and domain-invariant priors, enhancing generalizability. During sampling, the globally sensitive transformer-based diffusion model exploits the cross-distribution prior within the unified stochastic interpolant framework, enabling flexible and stable control over multi-distribution-to-noise interpolation paths and decoupled sampling strategies, thereby improving adaptation to OOD reconstruction. By alternating between data fidelity and sampling updates, our model achieves state-of-the-art performance with superior detail preservation in SVCT reconstructions. Extensive experiments demonstrate that CDPIR significantly outperforms existing approaches, particularly under OOD conditions, highlighting its robustness and potential clinical value in challenging imaging scenarios.