State-of-the-art deep learning systems such as TensorFlow and PyTorch tightly couple the model with the underlying hardware. This coupling requires the user to modify application logic in order to run the same job across a different set of resources, thereby limiting the choice of hardware for a given workload and potentially forcing the user to forgo more efficient hardware configurations. We propose VirtualFlow, a system leveraging a novel abstraction called virtual node processing to decouple the model from the hardware. In each step of training or inference, the batch of input data is split across virtual nodes instead of hardware accelerators (e.g. GPUs and TPUs). Mapping multiple virtual nodes to each accelerator and processing them sequentially effectively time slices the batch, thereby allowing users to reduce the memory requirement of their workloads and mimic large batch sizes on small clusters. Using this technique, VirtualFlow enables many new use cases, such as reproducing training results across different hardware, resource elasticity, and heterogeneous training. In our evaluation, our implementation of VirtualFlow for TensorFlow achieved strong convergence guarantees across different hardware with out-of-the-box hyperparameters, up to 48% lower job completion times with resource elasticity, and up to 42% higher throughput with heterogeneous training.