This work develops a Bayesian non-parametric approach to signal separation where the signals may vary according to latent variables. Our key contribution is to augment Gaussian Process Latent Variable Models (GPLVMs) for the case where each data point comprises the weighted sum of a known number of pure component signals observed across several input locations.Our framework allows arbitrary non-linear variations in the signals while being able to incorporate useful priors for the linear weights, such as including a sum-to-one constraint. Our contributions are particularly relevant to spectroscopy, where changing conditions may cause the underlying pure component signals to vary from sample to sample.To demonstrate the uses of our model we compare our method to alternatives on several simulated and real datasets.