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Leveraging spatial sparsity has become a popular approach to accelerate 3D computer graphics applications. Spatially sparse data structures and efficient sparse kernels (such as parallel stencil operations on active voxels), are key to achieve high performance. Existing work focuses on improving performance within a single sparse computational kernel. We show that a system that looks beyond a single kernel, plus additional domain-specific sparse data structure analysis, opens up exciting new space for optimizing sparse computations. Specifically, we propose a domain-specific data-flow graph model of imperative and sparse computation programs, which describes kernel relationships and enables easy analysis and optimization. Combined with an asynchronous execution engine that exposes a wide window of kernels, the inter-kernel optimizer can then perform effective sparse computation optimizations, such as eliminating unnecessary voxel list generations and removing voxel activation checks. These domain-specific optimizations further make way for classical general-purpose optimizations that are originally challenging to directly apply to computations with sparse data structures. Without any computational code modification, our new system leads to $4.02\times$ fewer kernel launches and $1.87\times$ speed up on our GPU benchmarks, including computations on Eulerian grids, Lagrangian particles, meshes, and automatic differentiation.