Sparse tensors are prevalent in many data-intensive applications. However, existing automatic differentiation (AD) frameworks are tailored towards dense tensors, which makes it a challenge to efficiently compute gradients through sparse tensor operations. This is due to irregular sparsity patterns that can result in substantial memory and computational overheads. We propose a novel framework that enables the efficient AD of sparse tensors. The key aspects of our work include a compilation pipeline leveraging two intermediate DSLs with AD-agnostic domain-specific optimizations followed by efficient C++ code generation. Our framework outperforms state-of-the-art alternatives across a variety of synthetic and real-world sparse tensor datasets.