Acquiring channel state information (CSI) through traditional methods, such as channel estimation, is increasingly challenging for the emerging sixth generation (6G) mobile networks due to high overhead. To address this issue, channel extrapolation techniques have been proposed to acquire complete CSI from a limited number of known CSIs. To improve extrapolation accuracy, environmental information, such as visual images or radar data, has been utilized, which poses challenges including additional hardware, privacy and multi-modal alignment concerns. To this end, this paper proposes a novel channel extrapolation framework by leveraging environment-related multi-path characteristics induced directly from CSI without integrating additional modalities. Specifically, we propose utilizing the multi-path characteristics in the form of power-delay profile (PDP), which is acquired using a CSI-to-PDP module. CSI-to-PDP module is trained in an AE-based framework by reconstructing the PDPs and constraining the latent low-dimensional features to represent the CSI. We further extract the total power & power-weighted delay of all the identified paths in PDP as the multi-path information. Building on this, we proposed a MAE architecture trained in a self-supervised manner to perform channel extrapolation. Unlike standard MAE approaches, our method employs separate encoders to extract features from the masked CSI and the multi-path information, which are then fused by a cross-attention module. Extensive simulations demonstrate that this framework improves extrapolation performance dramatically, with a minor increase in inference time (around 0.1 ms). Furthermore, our model shows strong generalization capabilities, particularly when only a small portion of the CSI is known, outperforming existing benchmarks.