While ML model training and inference are both GPU-intensive, CPU-based data processing is often the bottleneck. Distributed data processing systems based on the batch or stream processing models assume homogeneous resource requirements. They excel at CPU-based computation but either under-utilize heterogeneous resources or impose high overheads on failure and reconfiguration. We introduce the streaming batch model, a hybrid of the two models that enables efficient and fault-tolerant heterogeneous execution. The key idea is to execute one partition at a time to allow lineage-based recovery with dynamic resource allocation. This enables memory-efficient pipelining across heterogeneous resources, similar to stream processing, but also offers the elasticity and fault tolerance properties of batch processing. We present Ray Data, an implementation of the streaming batch model that improves throughput on heterogeneous batch inference pipelines by 3--8$\times$ compared to traditional batch and stream processing systems. When training Stable Diffusion, Ray Data matches the throughput of single-node ML data loaders while additionally leveraging distributed heterogeneous clusters to further improve training throughput by 31%.