Detection and prediction of combustion instabilities are of interest to the gas turbine engine community with many practical applications. This paper presents a dynamic data-driven approach to accurately detect precursors to the combustion instability phenomena. In particular, grey-scale images of combustion flames have been used in combination with pressure time-series data for information fusion to detect and predict flame instabilities in the combustion process. These grey-scale images are analyzed using deep belief network (DBN). The cross-dependencies between the features extracted by the DBN and the symbolic sequences generated from pressure time-series are then analyzed using ×D-Markov (pronounced cross D-Markov) models that are constructed by a combination of state-splitting and cross-entropy rate; this leads to the development of a variable-memory cross-model as a representation of the underlying physical process. These cross-models are then used for detection and prediction of combustion instability phenomena. The proposed concept is validated on experimental data collected from a laboratory-scale swirl-stabilized combustor apparatus, where the instability phenomena are induced by typical protocols leading to unstable flames.