Attention computation makes inference expensive in video diffusion transformers (vDiTs), which generate videos through iterative denoising. Block-sparse attention (BSA) reduces this cost by computing only blocks selected by a logical mask, which specifies attention interactions to compute. However, coupling logical block geometry to execution choices limits adaptation to varying masks and graphics processing units (GPUs), while runtime kernel specialization can incur preparation overhead that outweighs execution time savings. We present Tessera, a specialized runtime for dynamic BSA that decouples logical masks from GPU execution while preserving specified attention interactions. Its physical mapping layer retains, combines, or subdivides logical attention blocks into physical tiles suited to different attention mask shapes and GPU architectures. Its task organization layer groups and schedules tiles within GPU tasks to reuse data, expose parallelism, and overlap data movement with computation. Finally, profile-guided regime selection enables low- overhead execution plan selection through a lookup table constructed from offline profiling. We implement Tessera with specialized CUDA kernels supporting four NVIDIA GPU generations. Evaluated on 2,315 real attention masks and industrial video diffusion models, Tessera achieves up to 6.79x BSA request speedup over baseline systems in the evaluated video diffusion models.

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