Efficiency is essential to support ever-growing datasets, especially for Deep Learning (DL) systems. DL frameworks have traditionally embraced deferred execution-style DL code -- supporting symbolic, graph-based Deep Neural Network (DNN) computation. While scalable, such development is error-prone, non-intuitive, and difficult to debug. Consequently, more natural, imperative DL frameworks encouraging eager execution have emerged but at the expense of run-time performance. Though hybrid approaches aim for the "best of both worlds," using them effectively requires subtle considerations. Our key insight is that, while DL programs typically execute sequentially, hybridizing imperative DL code resembles parallelizing sequential code in traditional systems. Inspired by this, we present an automated refactoring approach that assists developers in determining which otherwise eagerly-executed imperative DL functions could be effectively and efficiently executed as graphs. The approach features novel static imperative tensor and side-effect analyses for Python. Due to its inherent dynamism, analyzing Python may be unsound; however, the conservative approach leverages a speculative (keyword-based) analysis for resolving difficult cases that informs developers of any assumptions made. The approach is: (i) implemented as a plug-in to the PyDev Eclipse IDE that integrates the WALA Ariadne analysis framework and (ii) evaluated on nineteen DL projects consisting of 132 KLOC. The results show that 326 of 766 candidate functions (42.56%) were refactorable, and an average relative speedup of 2.16x on performance tests was observed with negligible differences in model accuracy. The results indicate that the approach is useful in optimizing imperative DL code to its full potential.