We present a novel probabilistic deep learning approach, the 'Stochastic Latent Transformer' (SLT), designed for the efficient reduced-order modelling of stochastic partial differential equations. Stochastically driven flow models are pertinent to a diverse range of natural phenomena, including jets on giant planets, ocean circulation, and the variability of midlatitude weather. However, much of the recent progress in deep learning has predominantly focused on deterministic systems. The SLT comprises a stochastically-forced transformer paired with a translation-equivariant autoencoder, trained towards the Continuous Ranked Probability Score. We showcase its effectiveness by applying it to a well-researched zonal jet system, where the interaction between stochastically forced eddies and the zonal mean flow results in a rich low-frequency variability. The SLT accurately reproduces system dynamics across various integration periods, validated through quantitative diagnostics that include spectral properties and the rate of transitions between distinct states. The SLT achieves a five-order-of-magnitude speedup in emulating the zonally-averaged flow compared to direct numerical simulations. This acceleration facilitates the cost-effective generation of large ensembles, enabling the exploration of statistical questions concerning the probabilities of spontaneous transition events.