Changes in transcriptional regulatory networks can significantly alter cell fate. To gain insight into transcriptional dynamics, several studies have profiled bulk multi-omic data sets with parallel transcriptomic and epigenomic measurements at different stages of a developmental process. However, integrating these data to infer cell type-specific regulatory networks is a major challenge. We present dynamic regulatory module networks (DRMNs), a novel approach to infer cell type-specific -regulatory networks and their dynamics. DRMN integrates expression, chromatin state, and accessibility to predict -regulators of context-specific expression, where context can be cell type, developmental stage, or time point, and uses multitask learning to capture network dynamics across linearly and hierarchically related contexts. We applied DRMNs to study regulatory network dynamics in three developmental processes, each showing different temporal relationships and measuring a different combination of regulatory genomic data sets: cellular reprogramming, liver dedifferentiation, and forward differentiation. DRMN identified known and novel regulators driving cell type-specific expression patterns, showing its broad applicability to examine dynamics of gene regulatory networks from linearly and hierarchically related multi-omic data sets.