We introduce sum-product networks (SPNs) for robust speech processing through a simple robust automatic speaker identification (ASI) task.* SPNs are deep probabilistic graphical models capable of answering multiple probabilistic queries. We show that SPNs are able to remain robust by using the marginal probability density function (PDF) of the spectral features that reliably represent speech. Though current SPN toolkits and learning algorithms are in their infancy, we aim to show that SPNs have the potential to become a useful tool for robust speech processing in the future. SPN speaker models are evaluated here on real-world non-stationary and coloured noise sources at multiple signal-to-noise ratio (SNR) levels. In terms of ASI accuracy, we find that SPN speaker models are more robust than two recent convolutional neural network (CNN)-based ASI systems. Additionally, SPN speaker models consist of significantly fewer parameters than their CNN-based counterparts. The results indicate that SPN speaker models could be a robust, parameter-efficient alternative for ASI. Additionally, this work demonstrates that SPNs have potential in related tasks, such as robust automatic speech recognition (ASR) and automatic speaker verification (ASV).