In the wake of the burgeoning expansion of generative artificial intelligence (AI) services, the computational demands inherent to these technologies frequently necessitate cloud-powered computational offloading, particularly for resource-constrained mobile devices. These services commonly employ prompts to steer the generative process, and both the prompts and the resultant content, such as text and images, may harbor privacy-sensitive or confidential information, thereby elevating security and privacy risks. To mitigate these concerns, we introduce $Λ$-Split, a split computing framework to facilitate computational offloading while simultaneously fortifying data privacy against risks such as eavesdropping and unauthorized access. In $Λ$-Split, a generative model, usually a deep neural network (DNN), is partitioned into three sub-models and distributed across the user's local device and a cloud server: the input-side and output-side sub-models are allocated to the local, while the intermediate, computationally-intensive sub-model resides on the cloud server. This architecture ensures that only the hidden layer outputs are transmitted, thereby preventing the external transmission of privacy-sensitive raw input and output data. Given the black-box nature of DNNs, estimating the original input or output from intercepted hidden layer outputs poses a significant challenge for malicious eavesdroppers. Moreover, $Λ$-Split is orthogonal to traditional encryption-based security mechanisms, offering enhanced security when deployed in conjunction. We empirically validate the efficacy of the $Λ$-Split framework using Llama 2 and Stable Diffusion XL, representative large language and diffusion models developed by Meta and Stability AI, respectively. Our $Λ$-Split implementation is publicly accessible at https://github.com/nishio-laboratory/lambda_split.